Two independent random numbers x and y from anormal distribution with mean 0 and
Chapter 21, Problem 17(choose chapter or problem)
Two independent random numbers x and y from anormal distribution with mean 0 and standard deviation have joint density function p(x, y) =(1/(22)e(x2+y2)/(22). The average z = (x + y)/2has a one-variable probability density function of its own.(a) Give a double integral expression for F(t), the probabilitythat z t.(b) Give a single integral expression for F(t). To dothis, make the change of coordinates: u = (x+y)/2,v = (x y)/2 and then do the integral on dv. Usethe fact that ex2/a2dx = a.(c) Find the probability density function F(t) of z.(d) What is the name of the distribution of z?
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