Suppose X and Y Are Random Variables Is a Joint Density Function

question 42

Multiple Choice

Suppose X and Y are random variables. Find k such that the function $f ( x , y ) = \left\{ \begin{array} { c l } 0.1 e ^ { - ( \mid x + 0.4 y ) } & \text { if } x \geq 0 , y \geq 0 \\0 & \text { otherwise }\end{array} \right.$ is a joint density function.

• A)0.2
• B)2
• C)0.25
• D)1
• E)2.5
• F)0.4
• G)0.1
• H)0

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Definitions:

Critical Value

A threshold value that defines the boundary of the critical region, where if the test statistic exceeds this value, the null hypothesis is rejected.

Alpha

A threshold value used in hypothesis testing that represents the level of significance, typically set at 0.05 or 0.01, indicating the probability of wrongly rejecting the null hypothesis.

Chi-square Statistic

A statistical measure used to determine if there is a significant relationship between two categorical variables.

Degrees of Freedom

The number of independent values or quantities that can vary in the calculation of a statistic.