The Joint Density Function for a Pair of Random Variables

question 253

Essay

The joint density function for a pair of random variables X and Y is $f ( x , y ) = \left\{ \begin{array} { l l } C ( x + 1 ) & \text { if } 0 \leq x \leq 1 \text { and } 0 \leq y \leq 1 \\0 & \text { otherwise }\end{array} \right.$ (a) Find the value of C.(b) Find $P ( X + Y \leq 1 )$ .(c) Find $P ( X \leq 2 Y \leq 3 X )$ .

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Definitions:

Leverage

The use of borrowed funds to increase the potential return of an investment.

Return on Stockholders' Equity

A measure of financial performance calculated by dividing net income by average shareholders' equity, indicating how effectively equity is used to generate profit.

Price-Earnings Ratio

A ratio for valuing a company that measures its current share price relative to its per-share earnings.

Market Price

The existing rate at which a service or commodity can be acquired or disposed of.