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 + v2) 21 sx s 31, 21 s ys 31 f(x, y) = otherwise (a) Determine the conditional pdf of Y given that X = x. fyix(ylx) = for 21 sys 31 Determine the conditional pdf of X given that Y = y. for 21 sxs 31 (b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K = Round your answer to three decimal places.) 410,600 Compare this to P(Y 2 25). (Round your answer to three decimal places.) P(Y 2 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psi
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 + v2) 21 sx s 31, 21 s ys 31 f(x, y) = otherwise (a) Determine the conditional pdf of Y given that X = x. fyix(ylx) = for 21 sys 31 Determine the conditional pdf of X given that Y = y. for 21 sxs 31 (b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K = Round your answer to three decimal places.) 410,600 Compare this to P(Y 2 25). (Round your answer to three decimal places.) P(Y 2 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psi
A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Transcribed Image Text: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
f(x, y)
ĮK(x? + y?)
21 < x < 31, 21 < y < 31
%3|
otherwise
(a) Determine the conditional pdf of Y given that X = x.
fyix(y\x) =
for 21 < y < 31
%|
Determine the conditional pdf of X given that Y = y.
fXir(x\y) =
for 21 < x < 31
3
(b) If the pressure in the right tire is found to be 22 psi, what is the probability that the left tire has a pressure of at least 25 psi? (It is known that K
Round your answer to three decimal places.)
410,600
Compare this to P(Y > 25). (Round your answer to three decimal places.)
P(Y > 25) =
(c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K =
Round your answers to two decimal
410,600
places.)
expected pressure
psi
standard deviation
psi
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