Determine the probability density function for the random variable 1', when the probability density function of the random variable X and the bijective functional relationship 1' - 90?) are given. (a) The failure in electric circuits (in months) has an exponential distribution, Le. X ~E{l} with A = 0.05. What is the distribution of the maintenance costs, 1', for the company if 1' = 0.25 X Z + 2 X '? {b} Derive the probability density function for the general form of the normal distribution, is. Y~N{u, 0'2}, from probability density function of the standard normal distribution, Le. X~N{D,1}