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GATE 2021 | Statistics | Q-3
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GATE 2021 | Statistics | Q-11
Let $X$ be a non constant positive random variable such that $E(X)=9$. Then which of the following statements is correct A) $E(1X+1)>0.1$ and $P(X≥10)≤0.9$ B) $E(1X+1)<0.1$ and $P(X≥10)≤0.9$ C) $E(1X+1)>0.1$ and $P(X≥10)>0.9$ D) $E(1X+1)<0.1 and P(X≥10)>0.9$
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GATE 2016 | MATHS | Q-33
Suppose \( X \) and \( Y \) are two random variables such that \( aX + bY \) is a normal random variable for all \( a, b \) in \( \mathbf{R} \). Consider the following statements P, Q, R, and S: (P) : \( X \) is a standard normal random variable. (Q) ... 0. Which of the above statements ALWAYS hold TRUE? (A) both P and Q (B) both Q and R (C) both Q and S (D) both P and S
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GATE 2018 | MATH | Q-64
Let \(X_1\) and \(X_2\) be independent geometric random variables with the same probability mass function given by \(P(X = k) = p(1 - p)^{k-1}\), \(k = 1, 2, \ldots\). Then the value of \(P(X_1 = 2 | X_1 + X_2 = 4)\) correct up to three decimal places is____________
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GATE 2018 | MATHS | Q-62
Let $X1, X2, X3, X4$ be independent exponential random variables with mean $1, 1/2, 1/3, 1/4,$ respectively. Then $Y = min(X1, X2, X3, X4)$ has exponential distribution with mean equal to
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