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Recent questions tagged independent-events
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GATE ECE 2020 | Question: 25
The two sides of a fair coin are labelled as $0$ to $1$. The coin is tossed two times independently. Let $M$ and $N$ denote the labels corresponding to the outcomes of those tosses. For a random variable $X$, defined as $X = \text{min}(M, N)$, the expected value $E(X)$ (rounded off to two decimal places) is ___________.
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Probability and Statistics
Feb 13, 2020
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go_editor
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gate2020-ec
numerical-answers
probability-and-statistics
probability
independent-events
random-variable
expectation
0
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2
GATE ECE 2016 Set 3 | Question: 3
The probability of getting a “head” in a single toss of a biased coin is $0.3$. The coin is tossed repeatedly till a head is obtained. If the tosses are independent, then the probability of getting “head” for the first time in the fifth toss is _______
Milicevic3306
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Probability and Statistics
Mar 28, 2018
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Milicevic3306
15.8k
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112
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gate2016-ec-3
probability-and-statistics
probability
independent-events
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3
GATE ECE 2015 Set 1 | Question: 3
Suppose $A$ and $B$ are two independent events with probabilities $P(A) \neq 0$ and $P(B) \neq 0$. Let $\overline{A}$ and $\overline{B}$ be their complements. Which one of the following statements is FALSE? $P(A \cap B) = P(A)P(B)$ $P(A \mid B) = P(A)$ $P(A \cup B) = P(A) + P(B)$ $P(\overline{A} \cap \overline{B} )= P(\overline{A})P(\overline{B})$
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Probability and Statistics
Mar 28, 2018
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Milicevic3306
15.8k
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gate2015-ec-1
probability-and-statistics
probability
independent-events
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4
GATE ECE 2014 Set 3 | Question: 29
Let $X_{1},X_{2},$ and $X_{3}$ be independent and identically distributed random variables with the uniform distribution on $[0,1]$. The probability $P\left \{ X_{1}+X_{2}\leq X_{3}\right \}$ is _________.
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Probability and Statistics
Mar 26, 2018
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Milicevic3306
15.8k
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67
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gate2014-ec-3
probability-and-statistics
probability
independent-events
random-variable
uniform-distribution
numerical-answers
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5
GATE ECE 2013 | Question: 26
Let $U$ and $V$ be two independent zero mean Gaussian random variables of variances $\dfrac{1}{4}$ and $\dfrac{1}{9}$ respectively. The probability $P(3V\geq 2U)$ is $4/9$ $1/2$ $2/3$ $5/9$
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Probability and Statistics
Mar 26, 2018
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Milicevic3306
15.8k
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70
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gate2013-ec
probability-and-statistics
probability
random-variable
independent-events
0
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6
GATE ECE 2012 | Question: 24
Two independent random variables $X$ and $Y$ are uniformly distributed in the interval $[-1,1]$. The probability that max$[X,Y]$ is less than $\frac{1}{2}$ is $\frac{3}{4}$ $\frac{9}{16}$ $\frac{1}{4}$ $\frac{2}{3}$
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Probability and Statistics
Mar 25, 2018
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Milicevic3306
15.8k
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53
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gate2012-ec
probability-and-statistics
probability
independent-events
random-variable
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