Question

Each front tire on a particular type of 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 and Y for the left tire, the joint pdf
??,?(?,?)= ?(?^2 +?^?) ?? ?? ≤?≤ ??, ?? ≤?≤ ??

? ; ?????????

Where K is 3/380,000.

(a) What is the probability that both tires are underfilled (i.e. less than or equal to 26 psi)?

(b) What is marginal distribution of air pressure in the right tire alone?

(c) When Lisa checked, her right tire was at 25 psi. What is the probability density function of her left tire pressure knowing this?

(d) Are pressure tires of right and left (X, Y) independent? Prove independence/dependence.

Answer 1