# Question: Suppose is a random variable uniformly distributed over the

Suppose θ is a random variable uniformly distributed over the interval [0, 2π).

(a) Find the PDF of Y = sin (θ).

(b) Find the PDF of Z = cos (θ).

(c) Find the PDF of W = tan (θ).

(a) Find the PDF of Y = sin (θ).

(b) Find the PDF of Z = cos (θ).

(c) Find the PDF of W = tan (θ).

**View Solution:**## Answer to relevant Questions

A random variable has a CDF given by (a) Find the mean of X; (b) Find the variance of X; (c) Find the coefficient of skewness of X; (d) Find the coefficient of kurtosis of X. An exponential random variable has a PDF given by fX(x) = exp (– x) u (x) . (a) Find the mean and variance of X. (b) Find the conditional mean and the conditional variance given that X > 1 Let X be a standard normal random variable (i. e., X ~ N ( 0,1)). Find the PDF of Y= |X|. If the transformation is Suppose a random variable has some PDF given by fX(x). Find a function g(x) such that Y= g(X) is a uniform random variable over the interval (0, 1). Next, suppose that X is a uniform random variable. Find a function g(x) ...For the discrete random variables whose joint PMF is described find the following conditional PMFs: (a) PM (m |N = 2); (b) PM (m |N ≥ 2); (c) PM (m |N ≠ 2).Post your question