Question

U and v are two independent zero mean gaussian random variables of variances 1/4 and 1/ 9.

Answer 1

Since U and V are given to be normal random variables, therefore their difference will also be a normal random variable.

Here, let Y=3V-2U, where Y is also a normal random variable with mean = 0 and variance = 32 (1/9) + 22 (1/4) = 2

So it will be symmetric about mean that is 0.

P(Y>=0)= 1/2 (by symmetry property)

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