Each rear tire on an experimental airplane is supposed to be filled to a pressure of 36 pounds per square inch (psi). Let X denote the actual air pressure for the right tire and Y denote the actual air pressure for the left tire. Suppose that X and Y are random variables with the joint density function shown below. Complete parts (a) through (c). k(x² + y²), 30≤x≤42, 30 ≤ y < 42 0, elsewhere f(x,y)= (a) Find k. k= 1 376704 (b) Find P(32≤x≤34 and 37 ≤Y ≤40). ... 7,717 188,352 P(32 ≤ x ≤ 34 and 37 ≤ y ≤40) = (Simplify your answer.) (c) Find the probability that both tires are underfilled. The probability that both tires are underfilled is (Simplify your answer.)

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Each rear tire on an experimental airplane is supposed to be filled to a pressure of 36
pounds per square inch (psi). Let X denote the actual air pressure for the right tire and Y
denote the actual air pressure for the left tire. Suppose that X and Y are random
variables with the joint density function shown below. Complete parts (a) through (c).
(a) Find k.
k=
f(x,y) =
{a
1
376704
‹(x² + y²), 30≤x≤42, 30 ≤ y < 42
elsewhere
(b) Find P(32 ≤X ≤ 34 and 37 ≤ y ≤ 40).
7,717
188,352
P(32≤x≤ 34 and 37 ≤Y≤40) =
(Simplify your answer.)
(c) Find the probability that both tires are underfilled.
The probability that both tires are underfilled is
(Simplify your answer.)
▪
Transcribed Image Text:Each rear tire on an experimental airplane is supposed to be filled to a pressure of 36 pounds per square inch (psi). Let X denote the actual air pressure for the right tire and Y denote the actual air pressure for the left tire. Suppose that X and Y are random variables with the joint density function shown below. Complete parts (a) through (c). (a) Find k. k= f(x,y) = {a 1 376704 ‹(x² + y²), 30≤x≤42, 30 ≤ y < 42 elsewhere (b) Find P(32 ≤X ≤ 34 and 37 ≤ y ≤ 40). 7,717 188,352 P(32≤x≤ 34 and 37 ≤Y≤40) = (Simplify your answer.) (c) Find the probability that both tires are underfilled. The probability that both tires are underfilled is (Simplify your answer.) ▪
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