JK(x² + y²) f(x, y) = 0 20≤x≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K = (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.)
JK(x² + y²) f(x, y) = 0 20≤x≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K = (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.)
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 22PFA
Related questions
Question
please answer until (e)
Transcribed Image Text:Help with Symbolic Notation
Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 25 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
f(x, y) =
{K(2
JK(x² + y²)
20 ≤ x ≤ 30, 20 ≤ y ≤ 30
otherwise
(a) What is the value of K? (Enter your answer as a fraction.)
K=
(b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.)
(c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer
to four decimal places.)
(d) Determine the (marginal) distribution of air pressure in the right tire alone.
for 20≤x≤ 30
(e) Are X and Y independent rv's?
OYes, f(x, y) = fx(x) · fy(y), so X and Y are independent.
OYes, f(x,y) ‡ £x(x) · fy(y), so X and Y are independent.
ONO, f(x, y) = fx(x) · fy(y), so X and Y are not independent.
ONO, f(x, y) + fx(x) fy(y), so X and Y are not independent.
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