Find the Condition on the Non-Negative Constants a and B $p ( x , y ) = \left\{ \begin{array} { c l } a x + b y , & 0 \leq x \leq 8,0 \leq y \leq 8 \\0 & \text { otherwise }\end{array} \right.$

question 58

Multiple Choice

Find the condition on the non-negative constants a and b for p(x, y) to be a joint density function, where $p ( x , y ) = \left\{ \begin{array} { c l } a x + b y , & 0 \leq x \leq 8,0 \leq y \leq 8 \\0 & \text { otherwise }\end{array} \right.$

• A) \(a + b = \frac { 1 } { 256 }\)
• B) \(a + b = \frac { 1 } { 32 }\)
• C) \(a + b < \frac { 1 } { 256 }\)
• D)a=b
• E) \(a + b = \frac { 1 } { 512 }\)

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Definitions:

Income

The amount of money received over a period of time, usually from work, investments, or business activities.

Guiding Function

A principle or mechanism that directs actions or decisions towards a desired outcome or objective.

Market Conditions

Various factors and influences that affect the supply and demand of products and services within a market, including competition, consumer preference, and economic environment.

Changes In Prices

Variations in the cost of goods and services over time due to factors like inflation, supply and demand, or economic policies.