MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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) = 
 
K(x2 + y2)      19 ≤ x ≤ 29, 19 ≤ y ≤ 29
0   otherwise

(a) Determine the conditional pdf of Y given that X = x.

fY|X(y|x) =

 for 19 ≤ y ≤ 29

Determine the conditional pdf of X given that Y = y.

fX|Y(x|y) =

  for 19 ≤ x ≤ 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 

K = 
3
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? (It is known that 

K = 
3
350,600
.

 Round your answers to two decimal 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 19 < x < 29, 19 < y < 29 f(x, y) = {K(x2 + y²) otherwise (a) Determine the conditional pdf of Y given that X = x. for 19 < y < 29 |= (x1a}XU, Determine the conditional pdf of X given that Y = y. for 19 < x < 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 K = Round your answer to three decimal 350,600 places.) Compare this to P(Y 2 25). (Round your answer to three decimal places.) P(Y > 25) = 3 (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 350,600 your answers to two decimal places.) expected pressure psi standard deviation psi
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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 19 < x < 29, 19 < y < 29 f(x, y) = {K(x2 + y²) otherwise (a) Determine the conditional pdf of Y given that X = x. for 19 < y < 29 |= (x1a}XU, Determine the conditional pdf of X given that Y = y. for 19 < x < 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 K = Round your answer to three decimal 350,600 places.) Compare this to P(Y 2 25). (Round your answer to three decimal places.) P(Y > 25) = 3 (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 350,600 your answers to two decimal places.) expected pressure psi standard deviation psi
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