GO Electronics
Login
Register
Dark Mode
Brightness
Profile
Edit Profile
Messages
My favorites
My Updates
Logout
Filter
Recent
Hot!
Most votes
Most answers
Most views
Previous GATE
Featured
Highest voted questions in Engineering Mathematics
2
votes
0
answers
1
GATE ECE 2019 | Question: 1
Which one of the following functions is analytic over the entire complex plane? $\ln(z)$ $e^{1/z}$ $\frac{1}{1-z}$ $\cos(z)$
Which one of the following functions is analytic over the entire complex plane?$\ln(z)$$e^{1/z}$$\frac{1}{1-z}$$\cos(z)$
Arjun
6.5k
points
333
views
Arjun
asked
Feb 12, 2019
Complex Analysis
gate2019-ec
complex-analysis
+
–
1
votes
0
answers
2
TIFR ECE 2015 | Question: 2
Let $x[n]=a^{\lfloor n \mid}$, ( $a$ is real, $0<a<1$ ) and the discrete time Fourier transform $\text{(DTFT)}$ of $x[n]$ is given by $X(\omega)=\sum_{n=-\infty}^{\infty} x[n] e^{-j \omega n}$. Then the $\text{DTFT}$ ... zero only at one value of $\omega \in[-\pi, \pi]$ Its maximum value is larger than $1$ Its minimum value is less than $-1$ None of the above
Let $x[n]=a^{\lfloor n \mid}$, ( $a$ is real, $0<a<1$ ) and the discrete time Fourier transform $\text{(DTFT)}$ of $x[n]$ is given by $X(\omega)=\sum_{n=-\infty}^{\infty}...
admin
46.4k
points
99
views
admin
asked
Dec 15, 2022
Calculus
tifr2015
calculus
discrete-fourier-transform
+
–
1
votes
0
answers
3
TIFR ECE 2015 | Question: 6
$\textbf{A}$ is an $n \times n$ square matrix of reals such that $\mathbf{A y}=\mathbf{A}^{T} \mathbf{y}$, for all real vectors $\mathbf{y}$. Which of the following can we conclude? $\mathbf{A}$ is invertible $\mathbf{A}^{T}=\mathbf{A}$ $\mathbf{A}^{2}=\mathbf{A}$ Only (i) Only (ii) Only (iii) Only (i) and (ii) None of the above
$\textbf{A}$ is an $n \times n$ square matrix of reals such that $\mathbf{A y}=\mathbf{A}^{T} \mathbf{y}$, for all real vectors $\mathbf{y}$. Which of the following can w...
admin
46.4k
points
85
views
admin
asked
Dec 15, 2022
Linear Algebra
tifr2015
linear-algebra
matrices
+
–
1
votes
0
answers
4
TIFR ECE 2015 | Question: 7
Let $A$ be an $8 \times 8$ matrix of the form \[ \left[\begin{array}{cccc} 2 & 1 & \ldots & 1 \\ 1 & 2 & \ldots & 1 \\ \vdots & \vdots & \ddots & \vdots \\ 1 & 1 & \ldots & 2 \end{array}\ ... $\operatorname{det}(A)=9$ $\operatorname{det}(A)=18$ $\operatorname{det}(A)=14$ $\operatorname{det}(A)=27$ None of the above
Let $A$ be an $8 \times 8$ matrix of the form\[\left[\begin{array}{cccc}2 & 1 & \ldots & 1 \\1 & 2 & \ldots & 1 \\\vdots & \vdots & \ddots & \vdots \\1 & 1 & \ldots & 2\e...
admin
46.4k
points
110
views
admin
asked
Dec 15, 2022
Linear Algebra
tifr2015
linear-algebra
determinant
+
–
1
votes
0
answers
5
TIFR ECE 2015 | Question: 8
Let $X$ and $Y$ be two independent and identically distributed random variables. Let $Z=\max (X, Y)$ and $W=\min (X, Y)$. Which of the following is true? $Z$ and $W$ are independent $E(X Z)=E(Y W)$ $E(X Y)=E(Z W)$ $(a), (b)$, and $(c)$ $(a)$ and $(b)$ only
Let $X$ and $Y$ be two independent and identically distributed random variables. Let $Z=\max (X, Y)$ and $W=\min (X, Y)$. Which of the following is true?$Z$ and $W$ are i...
admin
46.4k
points
96
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
6
TIFR ECE 2015 | Question: 9
Consider a random variable $X$ that takes integer values $1$ through $10$ each with equal probability. Now consider random variable \[ Y=\min (7, \max (X, 4)). \] What is the variance of $Y?$ $121 / 4$ $37 / 20 $ $9 / 5$ $99 / 12$ None of the above
Consider a random variable $X$ that takes integer values $1$ through $10$ each with equal probability. Now consider random variable\[Y=\min (7, \max (X, 4)).\]What is the...
admin
46.4k
points
94
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
7
TIFR ECE 2015 | Question: 10
Let $X$ be a uniform random variable between $[0,1]$. And let \[ M=\min _{m X \geq 1, m \in \mathbb{N}} m . \] Then which of the following is true? $E(M)=\infty$ $E(M) \in[5,10]$ $E(M)=\exp (1)$ $E(M)=\pi$ None of the above
Let $X$ be a uniform random variable between $[0,1]$. And let\[M=\min _{m X \geq 1, m \in \mathbb{N}} m .\]Then which of the following is true?$E(M)=\infty$$E(M) \in[5,10...
admin
46.4k
points
84
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
8
TIFR ECE 2015 | Question: 13
Let \[ A=\left(\begin{array}{ccc} 1 & 1+\varepsilon & 1 \\ 1+\varepsilon & 1 & 1+\varepsilon \\ 1 & 1+\varepsilon & 1 \end{array}\right) \] Then for $\varepsilon=10^{-6}, A$ has only negative eigenvalues only non-zero eigenvalues only positive eigenvalues one negative and one positive eigenvalue None of the above
Let\[A=\left(\begin{array}{ccc}1 & 1+\varepsilon & 1 \\1+\varepsilon & 1 & 1+\varepsilon \\1 & 1+\varepsilon & 1\end{array}\right)\]Then for $\varepsilon=10^{-6}, A$ haso...
admin
46.4k
points
92
views
admin
asked
Dec 15, 2022
Linear Algebra
tifr2015
linear-algebra
eigen-values
+
–
1
votes
0
answers
9
TIFR ECE 2015 | Question: 14
Consider a frog that lives on two rocks $A$ and $B$ and moves from one rock to the other randomly. If it is at Rock $A$ at any time, irrespective of which rocks it occupied in the past, it jumps back to Rock $A$ with probability $2 / 3$ and instead jumps to Rock ... of $n$ jumps as $n \rightarrow \infty?$ $1 / 2 $ $2 / 3$ $1$ The limit does not exist None of the above
Consider a frog that lives on two rocks $A$ and $B$ and moves from one rock to the other randomly. If it is at Rock $A$ at any time, irrespective of which rocks it occupi...
admin
46.4k
points
88
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
conditional-probability
limits
+
–
1
votes
0
answers
10
TIFR ECE 2015 | Question: 15
Let $x_{1}=-1$ and $x_{2}=1$ be two signals that are transmitted with equal probability. If signal $x_{i}, i \in$ $\{1,2\}$ is transmitted, the received signal is $y=x_{i}+n_{i}$, where $n_{i}$ ... $\theta^{\star}$ to minimize the probability of error is $\leq 0$ None of the above.
Let $x_{1}=-1$ and $x_{2}=1$ be two signals that are transmitted with equal probability. If signal $x_{i}, i \in$ $\{1,2\}$ is transmitted, the received signal is $y=x_{i...
admin
46.4k
points
78
views
admin
asked
Dec 15, 2022
Probability and Statistics
tifr2015
probability-and-statistics
probability
normal-distribution
+
–
1
votes
0
answers
11
TIFR ECE 2014 | Question: 1
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0,1]$. For $\alpha \in[0,1]$, the probability that $\alpha \max (X, Y)<\min (X, Y)$ is $1 /(2 \alpha)$. $\exp (1-\alpha)$ $1-\alpha$ $(1-\alpha)^{2}$ $1-\alpha^{2}$
Consider two independent and identically distributed random variables $X$ and $Y$ uniformly distributed in $[0,1]$. For $\alpha \in[0,1]$, the probability that $\alpha \m...
admin
46.4k
points
112
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
uniform-distribution
+
–
1
votes
0
answers
12
TIFR ECE 2014 | Question: 2
Evaluate the limit \[ \lim _{n \rightarrow \infty}\left(2 n^{4}\right)^{\frac{1}{3 n}} . \] $e$ $1$ $2^{\frac{1}{3}}$ $0$ None of the above
Evaluate the limit\[\lim _{n \rightarrow \infty}\left(2 n^{4}\right)^{\frac{1}{3 n}} .\]$e$$1$$2^{\frac{1}{3}}$$0$None of the above
admin
46.4k
points
84
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
limits
+
–
1
votes
0
answers
13
TIFR ECE 2014 | Question: 3
For a non-negative continuous random variable $X$, which of the following is TRUE? $E\{X\}=\int_{0}^{\infty} P(X>x) d x$. $E\{X\}=\int_{0}^{\infty} P(X \leq x) d x$. $P(X<x) \leq \frac{E\{X\}}{x}$. $(a)$ and $(c)$. None of the above.
For a non-negative continuous random variable $X$, which of the following is TRUE?$E\{X\}=\int_{0}^{\infty} P(X>x) d x$.$E\{X\}=\int_{0}^{\infty} P(X \leq x) d x$.$P(X<x)...
admin
46.4k
points
96
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
14
TIFR ECE 2014 | Question: 5
The matrix \[ A=\left(\begin{array}{ccc} 1 & a_{1} & a_{1}^{2} \\ 1 & a_{2} & a_{2}^{2} \\ 1 & a_{3} & a_{3}^{2} \end{array}\right) \] is invertible when $a_{1}>a_{2}>a_{3}$ $a_{1}<a_{2}<a_{3}$ $a_{1}=3, a_{2}=2, a_{3}=4$ All of the above None of the above
The matrix\[A=\left(\begin{array}{ccc}1 & a_{1} & a_{1}^{2} \\1 & a_{2} & a_{2}^{2} \\1 & a_{3} & a_{3}^{2}\end{array}\right)\]is invertible when$a_{1}>a_{2}>a_{3}$$a_{1}...
admin
46.4k
points
83
views
admin
asked
Dec 14, 2022
Linear Algebra
tifr2014
linear-algebra
matrices
+
–
1
votes
0
answers
15
TIFR ECE 2014 | Question: 6
Let $g:[0, \pi] \rightarrow \mathbb{R}$ be continuous and satisfy \[ \int_{0}^{\pi} g(x) \sin (n x) d x=0 \] for all integers $n \geq 2$. Then which of the following can you say about $g?$ $g$ must be identically zero. $g(\pi / 2)=1$. $g$ need not be identically zero. $g(\pi)=0$. None of the above.
Let $g:[0, \pi] \rightarrow \mathbb{R}$ be continuous and satisfy\[\int_{0}^{\pi} g(x) \sin (n x) d x=0\]for all integers $n \geq 2$. Then which of the following can you ...
admin
46.4k
points
95
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
definite-integrals
+
–
1
votes
0
answers
16
TIFR ECE 2014 | Question: 7
Let $A$ be an $n \times n$ real matrix. It is known that there are two distinct $n$-dimensional real column vectors $v_{1}, v_{2}$ such that $A v_{1}=A v_{2}$. Which of the following can we conclude about $A?$ All eigenvalues of $A$ are non-negative. $A$ is not full rank. $A$ is not the zero matrix. $\operatorname{det}(A) \neq 0$. None of the above.
Let $A$ be an $n \times n$ real matrix. It is known that there are two distinct $n$-dimensional real column vectors $v_{1}, v_{2}$ such that $A v_{1}=A v_{2}$. Which of t...
admin
46.4k
points
113
views
admin
asked
Dec 14, 2022
Linear Algebra
tifr2014
linear-algebra
eigen-values
+
–
1
votes
0
answers
17
TIFR ECE 2014 | Question: 8
Consider a square pulse $g(t)$ of height $1$ and width $1$ centred at $1 / 2$. Define $f_{n}(t)=\frac{1}{n}\left(g(t) *^{n} g(t)\right),$ where $*^{n}$ stands for $n$-fold convolution. Let $f(t)=\lim _{n \rightarrow \infty} f_{n}(t)$. Then, which ... $\infty$. $f(t)$ has width $\infty$ and height $1$ . $f(t)$ has width $0$ and height $\infty$. None of the above.
Consider a square pulse $g(t)$ of height $1$ and width $1$ centred at $1 / 2$. Define $f_{n}(t)=\frac{1}{n}\left(g(t) *^{n} g(t)\right),$ where $*^{n}$ stands for $n$-fol...
admin
46.4k
points
93
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
limits
+
–
1
votes
0
answers
18
TIFR ECE 2014 | Question: 12
Assume that $Y, Z$ are independent, zero-mean, continuous random variables with variances $\sigma_{Y}^{2}$ and $\sigma_{Z}^{2},$ respectively. Let $X=Y+Z$. The optimal value of $\alpha$ which minimizes $\mathbb{E}\left[(X-\alpha Y)^{2}\right]$ ... $1$ $\frac{\sigma_{Y}^{2}}{\sigma_{Z}^{2}}$ None of the above.
Assume that $Y, Z$ are independent, zero-mean, continuous random variables with variances $\sigma_{Y}^{2}$ and $\sigma_{Z}^{2},$ respectively. Let $X=Y+Z$. The optimal va...
admin
46.4k
points
111
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
19
TIFR ECE 2014 | Question: 13
Let function $f: \mathbf{R} \rightarrow \mathbf{R}$ be convex, i.e., for $x, y \in \mathbf{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq$ $\alpha f(x)+(1-\alpha) f(y)$. Then which of the following is $\text{TRUE?}$ $f(x) \leq f(y)$ whenever ... $f$ and $g$ are both convex, then $\min \{f, g\}$ is also convex. For a random variable $X, E(f(X)) \geq f(E(X))$.
Let function $f: \mathbf{R} \rightarrow \mathbf{R}$ be convex, i.e., for $x, y \in \mathbf{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq$ $\alpha f(x)+(1-\alpha) f(y...
admin
46.4k
points
92
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
functions
+
–
1
votes
0
answers
20
TIFR ECE 2014 | Question: 14
Suppose that a random variable $X$ has a probability density function \[ \begin{aligned} f(x) & =c(x-4) \quad \text { for } 4 \leq x \leq 6 \\ & =0 \quad \text { for all other } x \end{aligned} \] for some constant $c$. What is the expected value of $X$ given that $X \geq 5?$ $5 \frac{5}{9}$ $5 \frac{1}{2}$ $5 \frac{3}{4}$ $5 \frac{1}{4}$ $5 \frac{5}{8}$
Suppose that a random variable $X$ has a probability density function\[\begin{aligned}f(x) & =c(x-4) \quad \text { for } 4 \leq x \leq 6 \\& =0 \quad \text { for all othe...
admin
46.4k
points
88
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
probability-density-function
+
–
1
votes
0
answers
21
TIFR ECE 2014 | Question: 16
A fair dice (with faces numbered $1, \ldots, 6$ ) is independently rolled twice. Let $X$ denote the maximum of the two outcomes. The expected value of $X$ is $4 \frac{1}{2}$ $3 \frac{1}{2}$ $5$ $4 \frac{17}{36} $ $4 \frac{3}{4}$
A fair dice (with faces numbered $1, \ldots, 6$ ) is independently rolled twice. Let $X$ denote the maximum of the two outcomes. The expected value of $X$ is$4 \frac{1}{2...
admin
46.4k
points
31
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
expectation
+
–
1
votes
0
answers
22
TIFR ECE 2014 | Question: 17
Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian distributed with mean $\mu_{2}$ and variance $\sigma_{2}^{2}$. Then the distribution ... variable with mean $\mu_{2}$ and variance $\sigma_{1}^{2}+\sigma_{2}^{2}$. Has no known form. None of the above.
Let $X$ be a Gaussian random variable with mean $\mu_{1}$ and variance $\sigma_{1}^{2}$. Now, suppose that $\mu_{1}$ itself is a random variable, which is also Gaussian d...
admin
46.4k
points
89
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
normal-distribution
+
–
1
votes
0
answers
23
TIFR ECE 2014 | Question: 18
A non-negative loss in a car accident is distributed with the following probability density function \[ f(x)=\frac{1}{10} \exp (-x / 10) \] for $x \geq 0$. Suppose that first $5$ units of loss is incurred by the insured and the remaining loss if any is covered by the ... $5+10 \exp \left(-\frac{1}{2}\right)$ $15 \exp \left(-\frac{1}{2}\right)$
A non-negative loss in a car accident is distributed with the following probability density function\[f(x)=\frac{1}{10} \exp (-x / 10)\]for $x \geq 0$. Suppose that first...
admin
46.4k
points
107
views
admin
asked
Dec 14, 2022
Probability and Statistics
tifr2014
probability-and-statistics
probability
probability-density-function
+
–
1
votes
0
answers
24
TIFR ECE 2014 | Question: 20
What is \[ \lim _{n \rightarrow \infty} \cos \frac{\pi}{2^{2}} \cos \frac{\pi}{2^{3}} \cdots \cos \frac{\pi}{2^{n}} ? \] $0$ $\pi / 2$ $1 / \sqrt{2}$ $2 / \pi$ None of the above.
What is\[\lim _{n \rightarrow \infty} \cos \frac{\pi}{2^{2}} \cos \frac{\pi}{2^{3}} \cdots \cos \frac{\pi}{2^{n}} ?\]$0$$\pi / 2$$1 / \sqrt{2}$$2 / \pi$None of the above....
admin
46.4k
points
82
views
admin
asked
Dec 14, 2022
Calculus
tifr2014
calculus
limits
+
–
1
votes
0
answers
25
TIFR ECE 2013 | Question: 4
Consider a fair coin that has probability $1 / 2$ of showing heads $(\text{H})$ in a toss and $1 / 2$ of showing tails $(\text{T})$. Suppose we independently flip a fair coin over and over again. What is the probability that $\text{HT}$ sequence occurs before $\text{TT}?$ $3 / 4$ $1 / 2$ $2 / 3$ $1 / 3$ $1 / 4$
Consider a fair coin that has probability $1 / 2$ of showing heads $(\text{H})$ in a toss and $1 / 2$ of showing tails $(\text{T})$. Suppose we independently flip a fair ...
admin
46.4k
points
78
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
26
TIFR ECE 2013 | Question: 9
Let $X$ and $Y$ be two zero mean independent continuous random variables. Let $Z_{1}=\max (X, Y)$, and $Z_{2}=\min (X, Y)$. Then which of the following is TRUE. $Z_{1}$ and $Z_{2}$ are uncorrelated. $Z_{1}$ and $Z_{2}$ are independent. $P\left(Z_{1}=Z_{2}\right)=\frac{1}{2}$. Both $(a)$ and $(c)$ Both $(a)$ and $(b)$
Let $X$ and $Y$ be two zero mean independent continuous random variables. Let $Z_{1}=\max (X, Y)$, and $Z_{2}=\min (X, Y)$. Then which of the following is TRUE.$Z_{1}$ an...
admin
46.4k
points
68
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
27
TIFR ECE 2013 | Question: 10
Consider the following series of square matrices: \[ \begin{array}{l} H_{1}=[1], \\ H_{2}=\left[\begin{array}{cc} 1 & 1 \\ 1 & -1 \end{array}\right], \end{array} \] and for $k=2,3, \ldots$, the $2^{k} \times 2^{k}$ matrix $H_{2^{k}}$ is recursively defined as \[ H_{2^{k}}=\ ... is $H_{2^{k}} H_{2^{k}}^{T}?)$ $0$ $2^{k}$ $2^{k / 2}$ $2^{k 2^{k-1}}$ $2^{k 2^{k}}$
Consider the following series of square matrices:\[\begin{array}{l}H_{1}= , \\H_{2}=\left[\begin{array}{cc}1 & 1 \\1 & -1\end{array}\right],\end{array}\]and for $k=2,3, \...
admin
46.4k
points
37
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
determinant
+
–
1
votes
0
answers
28
TIFR ECE 2013 | Question: 11
Two matrices $A$ and $B$ are called similar if there exists another matrix $S$ such that $S^{-1} A S=B$. Consider the statements: If $A$ and $B$ are similar then they have identical rank. If $A$ and $B$ ... Both $\text{I}$ and $\text{II}$ but not $\text{III}$. All of $\text{I}, \text{II}$ and $\text{III}$.
Two matrices $A$ and $B$ are called similar if there exists another matrix $S$ such that $S^{-1} A S=B$. Consider the statements:If $A$ and $B$ are similar then they have...
admin
46.4k
points
76
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
rank-of-matrix
+
–
1
votes
0
answers
29
TIFR ECE 2013 | Question: 12
Let $A$ be a Hermitian matrix and let $I$ be the Identity matrix with same dimensions as $A$. Then for a scalar $\alpha>0, A+\alpha I$ has the same eigenvalues as of $A$ but different eigenvectors the same eigenvalues and eigenvectors as of ... those of $A$ and same eigenvectors as of $A$ eigenvalues and eigenvectors with no relation to those of $A$ None of the above
Let $A$ be a Hermitian matrix and let $I$ be the Identity matrix with same dimensions as $A$. Then for a scalar $\alpha>0, A+\alpha I$ hasthe same eigenvalues as of $A$ b...
admin
46.4k
points
38
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
eigen-values
+
–
1
votes
0
answers
30
TIFR ECE 2013 | Question: 13
Let $A$ be a square matrix and $x$ be a vector whose dimensions match $A$. Let $B^{\dagger}$ be the conjugate transpose of $B$. Then which of the following is not true: $x^{\dagger} A^{2} x$ is always non-negative $x^{\dagger} A x$ ... $A=A^{\dagger}$ then $x^{\dagger} A y$ is complex for some vector $y$ with same dimensions as $x$
Let $A$ be a square matrix and $x$ be a vector whose dimensions match $A$. Let $B^{\dagger}$ be the conjugate transpose of $B$. Then which of the following is not true:$x...
admin
46.4k
points
38
views
admin
asked
Dec 12, 2022
Linear Algebra
tifr2013
linear-algebra
matrices
+
–
1
votes
0
answers
31
TIFR ECE 2013 | Question: 14
$X, Y, Z$ are integer valued random variables with the following two properties: $X$ and $Y$ are independent. For all integer $x$, conditioned on the event $\{X=x\}$, we have that $Y$ and $Z$ are independent (in other words, conditioned on ... and $Z$ are independent Conditioned on $Z$, the random variables $X$ and $Y$ are independent All of the above None of the above
$X, Y, Z$ are integer valued random variables with the following two properties:$X$ and $Y$ are independent.For all integer $x$, conditioned on the event $\{X=x\}$, we ha...
admin
46.4k
points
39
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
32
TIFR ECE 2013 | Question: 16
A surprise quiz contains three multiple choice questions; question $1$ has $3$ suggested answers, question $2$ has four, and question $3$ has two. A completely unprepared student decides to choose the answers at random. If $X$ is the number of questions the student answers ... expected number of correct answers is $15 / 12$ $7 / 12$ $13 / 12$ $18 / 12$ None of the above
A surprise quiz contains three multiple choice questions; question $1$ has $3$ suggested answers, question $2$ has four, and question $3$ has two. A completely unprepared...
admin
46.4k
points
68
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
33
TIFR ECE 2013 | Question: 17
Consider four coins, three of which are fair, that is they have heads on one side and tails on the other and both are equally likely to occur in a toss. The fourth coin has heads on both sides. Given that one coin amongst the four is picked at random and is tossed, and the ... is the probability that its other side is tails? $1 / 2$ $3 / 8$ $3 / 5$ $3 / 4$ $5 / 7$
Consider four coins, three of which are fair, that is they have heads on one side and tails on the other and both are equally likely to occur in a toss. The fourth coin h...
admin
46.4k
points
37
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
random-variable
+
–
1
votes
0
answers
34
TIFR ECE 2013 | Question: 18
Consider a coin tossing game between Santa and Banta. Both of them toss two coins sequentially, first Santa tosses a coin then Banta and so on. Santa tosses a fair coin: Probability of heads is $1 / 2$ and probability of tails is $1 / 2$. Banta's coin probabilities depend on ... the two trials conducted by each of them? $1 / 2$ $5 / 16$ $3 / 16$ $1 / 4$ $1 / 3$
Consider a coin tossing game between Santa and Banta. Both of them toss two coins sequentially, first Santa tosses a coin then Banta and so on. Santa tosses a fair coin: ...
admin
46.4k
points
46
views
admin
asked
Dec 12, 2022
Probability and Statistics
tifr2013
probability-and-statistics
probability
conditional-probability
+
–
1
votes
0
answers
35
TIFR ECE 2013 | Question: 19
Which of the following is true for polynomials defined over real numbers $\mathbb{R}$. Every odd degree polynomial has a real root. Every odd degree polynomial has at least one complex root. Every even degree polynomial has at least one complex root. Every even degree polynomial has a real root. None of the above
Which of the following is true for polynomials defined over real numbers $\mathbb{R}$.Every odd degree polynomial has a real root.Every odd degree polynomial has at least...
admin
46.4k
points
35
views
admin
asked
Dec 12, 2022
Calculus
tifr2013
calculus
polynomials
+
–
1
votes
0
answers
36
TIFR ECE 2013 | Question: 20
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$. Which of the following is not convex: $x^{2}$ $x^{3}$ $x$ $x^{4}$ $\mathrm{e}^{x}$
A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$.Which...
admin
46.4k
points
89
views
admin
asked
Dec 12, 2022
Calculus
tifr2013
calculus
functions
+
–
1
votes
0
answers
37
TIFR ECE 2012 | Question: 1
The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is $\ln \left(1+e^{-1 / 4}\right)$ $\ln (5 / 3)$ $0$ $\ln \left(1+e^{2}\right)$ None of the above
The minimum value of $f(x)=\ln \left(1+\exp \left(x^{2}-3 x+2\right)\right)$ for $x \geq 0$, where $\ln (\cdot)$ denotes the natural logarithm, is$\ln \left(1+e^{-1 / 4}\...
admin
46.4k
points
114
views
admin
asked
Dec 8, 2022
Calculus
tifr2012
calculus
maxima-minima
+
–
1
votes
0
answers
38
TIFR ECE 2012 | Question: 2
Let $\alpha_{1}, \alpha_{2}, \cdots, \alpha_{k}$ be complex numbers. Then \[ \lim _{n \rightarrow \infty}\left|\sum_{i=1}^{k} \alpha_{i}^{n}\right|^{1 / n} \] is $0$ $\infty$ $\alpha_{k}$ $\alpha_{1}$ $\max _{j}|\alpha_{j}|$
Let $\alpha_{1}, \alpha_{2}, \cdots, \alpha_{k}$ be complex numbers. Then\[\lim _{n \rightarrow \infty}\left|\sum_{i=1}^{k} \alpha_{i}^{n}\right|^{1 / n}\]is$0$$\infty$$\...
admin
46.4k
points
86
views
admin
asked
Dec 8, 2022
Calculus
tifr2012
calculus
limits
+
–
1
votes
0
answers
39
TIFR ECE 2012 | Question: 10
Suppose three dice are rolled independently. Each dice can take values $1$ to $6$ with equal probability. Find the probability that the second highest outcome equals the average of the other two outcomes. Here, the ties may be resolved arbitrarily. $1 / 6$ $1 / 9$ $39 / 216$ $7 / 36$ $43 / 216$
Suppose three dice are rolled independently. Each dice can take values $1$ to $6$ with equal probability. Find the probability that the second highest outcome equals the ...
admin
46.4k
points
80
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
independent-events
+
–
1
votes
0
answers
40
TIFR ECE 2012 | Question: 11
A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales as $\lambda$ $\lambda^{2}$ $\lambda^{3}$ $\sqrt{\lambda}$ None of the above
A Poisson random variable $X$ is given by $\operatorname{Pr}\{X=k\}=\mathrm{e}^{-\lambda} \lambda^{k} / k !, k=0,1,2, \ldots$ for $\lambda>0$. The variance of $X$ scales ...
admin
46.4k
points
70
views
admin
asked
Dec 8, 2022
Probability and Statistics
tifr2012
probability-and-statistics
probability
poisson-distribution
+
–
Page:
1
2
3
4
...
10
next »
GO Electronics
Email or Username
Show
Hide
Password
I forgot my password
Remember
Log in
Register