Recent questions tagged probability-and-statistics

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Let $X\in \{0,1\}$ and $Y\in \{0,1\}$ be two independent binary random variables. If $P(X=0)=p$ and $P(Y=0)=q,$ then $P(X+Y\geq 1)$ is equal to$pq+(1-p)(1-q)$$pq$$p(1-q)$...
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Consider the $Z$-channel given in the figure. The input is $0$ or $1$ with equal probability.If the output is $0$, the probability that the input is also $0$ equals _____...
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An unbiased coin is tossed an infinite number of times. The probability that the fourth head appears at the tenth toss is$0.067$$0.073$$0.082$$0.091$
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A fair coin is tossed till head appears for the first time. The probability that the number of required tosses is odd, is$\frac{1}{3}$$\frac{1}{2}$$\frac{2}{3}$$\frac{3}{...
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Let $X_{1},\:X_{2},\:X_{3}$ and $X_{4}$ be independent normal random variable with zero mean and unit variance. The probability that $X_{4}$ is the smallest among the fou...
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Three fair cubical dice are thrown simultaneously . The probability that all three dice have the same number of dots on the faces showing up is (up to third decimal place...