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- right tire and Y for the left tire, with joint pdf + y?) 19 sx s 29, 19 < y s 29 f(x, y) = otherwise (a) Determine the conditional pdf of Y given that X = x. fyx(y\x) = for 19 sy s 29 Determine the conditional pdf of X given that Y = y. fXiy(x\y) = for 19 s x s 29 (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
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- right tire and Y for the left tire, with joint pdf + y?) 19 sx s 29, 19 < y s 29 f(x, y) = otherwise (a) Determine the conditional pdf of Y given that X = x. fyx(y\x) = for 19 sy s 29 Determine the conditional pdf of X given that Y = y. fXiy(x\y) = for 19 s x s 29 (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
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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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
K(x² +
19 < x < 29, 19 < y < 29
f(x, у) %3D
otherwise
(a) Determine the conditional pdf of Y given that X = x.
fyxCylx) =
for 19 < y s 29
Determine the conditional pdf of X given that Y = y.
fxin(x\y) =
for 19 < x S 29
(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
3
K =
350,600
Round your answer to three decimal places.)
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?
3
(It is known that K =
Round your answers to two decimal places.)
350,600
expected pressure
psi
standard deviation
psi
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