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

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 tire and Y for
the left tire, with joint pdf given below.
f(x, y) =
K(x2 + y2)
22 ≤ x ≤ 32, 22 ≤ y ≤ 32
0
otherwise
(a) Compute the covariance between X and
Y.
(b) Compute the correlation coefficient p...

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c. 0.58
d. 1.44
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A hint is given =norm.dist(x,mean,stdev,true) To get
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???ALASKA AIRLINES: NAVIGATING CHANGE
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