WW09: Problem 24 (1 point) () (a) Find the indefinite integrals below, noting that the expression...

Transcribed Image Text:

WW09: Problem 24 (1 point) () (a) Find the indefinite integrals below, noting that the expression e-4 (A cos(mx) + B sin(mx)) might be relevant: 4x Answer: Se4* sin(m) da = Answer: Se cos(mx) dx = (b) A random variable Y has an exponential distribution, with the probability density shown here: 4e-4y, for y 0, p(y) = 0, for y < 0. Find the expected value of the random variable X = 3 cos(2Y) - sin(2Y). Answer: E[X]=E[3 cos(2Y) - sin(2Y)] = 00 Hint: For any given random variable Y and function h, E[h(Y)] = [ h(y)p(y) dy. This woohlam WW09: Problem 24 (1 point) () (a) Find the indefinite integrals below, noting that the expression e-4 (A cos(mx) + B sin(mx)) might be relevant: 4x Answer: Se4* sin(m) da = Answer: Se cos(mx) dx = (b) A random variable Y has an exponential distribution, with the probability density shown here: 4e-4y, for y 0, p(y) = 0, for y < 0. Find the expected value of the random variable X = 3 cos(2Y) - sin(2Y). Answer: E[X]=E[3 cos(2Y) - sin(2Y)] = 00 Hint: For any given random variable Y and function h, E[h(Y)] = [ h(y)p(y) dy. This woohlam