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.)
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.)
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 29CR
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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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