Let X and Y are independent normal random variables with mean 0 and variances 1 and 4 respectively. (a) What is P(Y > X + 3)? (b) What is the joint density function of X and Y ? (c) If (R, Θ) are the...

Let X and Y are independent normal random variables with mean 0 and variances 1 and 4 respectively.

(a) What is P(Y > X + 3)?

(b) What is the joint density function of X and Y ?

(c) If (R, Θ) are the polar coordinates of (X, Y ) (that is, R = √ X2 + Y 2 and Θ is the solution to R cos Θ = X and R sin Θ = Y ) then what is the joint density function of R and Θ?

(d) Calculate the marginal density function of Θ.

please answer all parts