GATE | GATE CS 2008 | Question 29

Let X be a random variable following normal distribution with mean +1 and variance 4. Let Y be another normal variable with mean -1 and variance unknown If P(X <=-1) = P(Y >-2). the standard deviation of Y is
(A) 3
(B) 2
(C) sqrt(2)
(D) 1


Answer: (A)

Explanation:  X(1, 4), Y(-1, \triangledown^{2})  P(X\leq -1) Z = \frac{-1-1}{2} = -1  = P(Z< \leq -1) = P(Z \geq 1) = 0.5 - P(0<Z<1)  = 0.5 -0.3413 = 0.1587  If \triangledown = 3, then \hspace{0.2cm} P(Z\geq 2), Z=\frac{2+1}{3} = 1  = P(Z\geq 1) = 0.1587

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