Project ForgeDiscrete Mathematics
Probability & Combinatorics
GATE 2008
Hard
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
- 3
- B2
- C√2
- D1
Explanation
For X (mean 1, sd 2): P(X≤-1) = P(Z≤(-1-1)/2) = P(Z≤-1) = P(Z≥1) by symmetry. For Y (mean -1, sd σ): P(Y≥2) = P(Z≥(2-(-1))/σ) = P(Z≥3/σ). Setting these equal: P(Z≥3/σ)=P(Z≥1) requires 3/σ=1, so σ=3.
Source: GATE CS 2008 (2008)
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