1. The random variable X is Gaussian with mean 3 and variance 4; that is X ~ N(3,4). $x() = veze sve [5] (a) Find P(-1 < X < 5), the probability that X is between -1 and 5 (inclusive). Write your answer in terms of the 0 () function. [5] (b) Find P(X2 3 < 6). Write your answer in terms of the 0 () function. [5] (c) We know from class that the random variable Y = 2X + 4 is Gaussian. Find fy(y), the probability density function of Y. [10] (d) Let Z = X?. Find fz(z), the probability density function of Z.

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