Answer the following quesion as much as possible. Thank you!

(b) 10 points The normal distribution Normal(m, v) with mean m E R and variance v > ( has Lebesgue density exp(-(y - m)-/(2v))/v2av,y E R, and Fourier transformation exp(imt - gut? ), tER. Assume Y = 2Y1 - 3)2 + Ya where Y1, Y2, Ya are independent random variables with C(Y) = C(Y2) = [(Y3) = Normal(2, 1). Find (i) the characteristic function and (ii) the Lebesgue density of Y