The Joint Pdf of Pressures for Right (X) and Left

question 6

Essay

The joint pdf of pressures for right (X) and left (Y) front tires is given by $f ( x , y ) = \left\{ \begin{array} { c l } K \left( x ^ { 2 } + y ^ { 2 } \right) & 20 \leq x \leq 30,20 \leq y \leq 30 \\0 & \text { otherwise }\end{array} \right.$ .
a. Determine the conditional pdf of Y given that X = x and the conditional pdf of X given that Y = y if you are given $F _ { X } ( x ) = 10 \mathrm { kx } ^ { 2 } + .05 \text { for } 20 \leq x \leq 30 \text { and } F _ { Y } ( y ) = 10 \mathrm {~ky} ^ { 2 } + .05 \text { for } 20 \leq y \leq 30$
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? Compare this to $P ( Y \geq 25 )$
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?

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Definitions:

Episodic Memory

A category of long-term memory that involves the recollection of specific events, situations, and experiences, including the context and emotions associated with them.

Semantic

Relating to meaning in language or logic, particularly the relationship between signs and symbols and what they represent.

Episodic

Related to or consisting of distinct and separate parts or events, often used in the context of memory to describe personal experiences that can be explicitly stated.

Procedural

Related to processes and methods of performing tasks, often implying a sequence of actions or steps.