. Each front tire of a vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable—X for the right tire and Y for the left tire, with...

. Each front tire of a vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air

pressure in each tire is a random variable—X for the right tire and Y for the left tire, with joint pdf

f ðx; yÞ ¼

k x2 þ y2 ð Þ 20 _ x _ 30, 20 _ y _ 30

0 otherwise

_

(a) What is the value of k?

(b) What is the probability that both tires are underfilled?

(c) What is the probability that the difference in air pressure between the two tires is at most 2 psi?

(d) Determine the (marginal) distribution of air pressure in the right tire alone.

(e) Are X and Y independent rvs?