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 pdff(x, y) = K(x2 + y2) 19 ≤ x ≤ 29, 19 ≤ y ≤ 290 otherwise(a) Determine the conditional pdf of Y given that X = x.fY|X(y|x) = for 19 ≤ y ≤ 29Determine 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 = 3350,600. 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 = 3350,600. Round your answers to two decimal places.)expected pressure psistandard 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 jointpdf19 < x < 29, 19 < y < 29f(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 decimal350,600places.)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 =Round350,600your answers to two decimal places.)expected pressurepsistandard deviationpsi

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College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 39E: Assume that the probability that an airplane engine will fail during a torture test is 12and that...

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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.

f_Y|X(y|x) =

for 19 ≤ y ≤ 29

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

f_X|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 =

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 =

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

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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