f(x, y) = = {x(x² + y²) +y²) 20 ≤x≤ 30, 20 ≤ y ≤ 30 otherwise (a) Determine the conditional pdf of Y given that X = x. fylx(ylx) = for 20 ≤ y ≤ 30 Determine the conditional pdf of X given that Y= y. fxy(xly) = for 20 ≤ x ≤ 30 (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 = 380,000 Round your answer to three decimal places.)
f(x, y) = = {x(x² + y²) +y²) 20 ≤x≤ 30, 20 ≤ y ≤ 30 otherwise (a) Determine the conditional pdf of Y given that X = x. fylx(ylx) = for 20 ≤ y ≤ 30 Determine the conditional pdf of X given that Y= y. fxy(xly) = for 20 ≤ x ≤ 30 (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 = 380,000 Round your answer to three decimal places.)
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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![**Probability and Statistics: Tire Pressure Example**
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 probability density function (pdf)
\[ f(x, y) =
\begin{cases}
K(x^2 + y^2) & \text{for } 20 \leq x \le 30, 20 \le y \le 30 \\
0 & \text{otherwise}
\end{cases}
\]
(a) Determine the conditional pdf of \( Y \) given that \( X = x \).
\[
f_{Y|X}(y|x) = \boxed{\phantom{f_{Y|X}(y|x) = }} \text{for } 20 \leq y \le 30
\]
Determine the conditional pdf of \( X \) given that \( Y = y \).
\[
f_{X|Y}(x|y) = \boxed{\phantom{f_{X|Y}(x|y) = }} \text{for } 20 \leq x \le 30
\]
(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 \( K = \frac{3}{380,000} \)). Round your answer to three decimal places.
\[
\boxed{\phantom{abcde}}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18694516-cac0-450c-bfd2-4a4488b9c5fd%2F74ae2ccb-b2e7-4612-82a6-5cbb5e483baa%2Fdphnzab_processed.png&w=3840&q=75)
Transcribed Image Text:**Probability and Statistics: Tire Pressure Example**
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 probability density function (pdf)
\[ f(x, y) =
\begin{cases}
K(x^2 + y^2) & \text{for } 20 \leq x \le 30, 20 \le y \le 30 \\
0 & \text{otherwise}
\end{cases}
\]
(a) Determine the conditional pdf of \( Y \) given that \( X = x \).
\[
f_{Y|X}(y|x) = \boxed{\phantom{f_{Y|X}(y|x) = }} \text{for } 20 \leq y \le 30
\]
Determine the conditional pdf of \( X \) given that \( Y = y \).
\[
f_{X|Y}(x|y) = \boxed{\phantom{f_{X|Y}(x|y) = }} \text{for } 20 \leq x \le 30
\]
(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 \( K = \frac{3}{380,000} \)). Round your answer to three decimal places.
\[
\boxed{\phantom{abcde}}
\]
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