A given car company set a standard that for each tire should be filled to a pressure of 40 psi. Given X and Y are random variables and X denotes the actual pressure on the front tires and Y denotes the actual pressure on the back tires. Their joint density function is given by f(x, y) = {0(x* + y*), 30 sxs 50, 30 s y s 50 elsewhere a. Find the value of the constant Q. b. Find P(30 < x S 40,40 < Y < 50) c. Find the probability that both of the tires have insufficient amount of pressure

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A given car company set a standard that for each tire should be filled to a pressure of
40 psi. Given X and Y are random variables and X denotes the actual pressure on the front tires
and Y denotes the actual pressure on the back tires. Their joint density function is given by
f(x,y) = {O(x² + y²),
30 sxs 50, 30 < y s 50
elsewhere
a. Find the value of the constant Q.
b. Find P(30 < X < 40 , 40 < Y < 50)
c. Find the probability that both of the tires have insufficient amount of pressure
Transcribed Image Text:A given car company set a standard that for each tire should be filled to a pressure of 40 psi. Given X and Y are random variables and X denotes the actual pressure on the front tires and Y denotes the actual pressure on the back tires. Their joint density function is given by f(x,y) = {O(x² + y²), 30 sxs 50, 30 < y s 50 elsewhere a. Find the value of the constant Q. b. Find P(30 < X < 40 , 40 < Y < 50) c. Find the probability that both of the tires have insufficient amount of pressure
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