Given a Gaussiandistributed random variable X whose pdf is g

Given a Gaussian-distributed random variable X, whose pdf is given as, f_x (x) = 1/squareroot 8pi exp (-(x-3)^2/8) Find the mean, variance and probability of the random variable E{X}= Var{X}= P{x lessthanorequalto 3} Now, we form a new random variable Y = aX-b, with parameters a = 0.5 and b = 15. Find the pdf of, i.e. P_r(y)=? Find the following statistics using the results from the above: E{aX-b}= Var{aX-b}=

Solution

the following statistics using the result from the symeetry

symemetry =0

for (ax-b)-ay-b)

e(x2)-e(x2)

var (ax-b)-(bx-c)