Let X and Y Be Two Independent Random Variables with the Following

question 25

Essay

Let X and Y be two independent random variables with the following probability distributions:
$\begin{array}{l}\begin{array} { l | r r r } x & 1 & 2 & 3 \\\hline p ( x ) & 0.2 & 0.5 & 0.3\end{array}\\\begin{array} { l | r r r } y & - 1 & 0 & 1 \\\hline p ( y ) & 0.3 & 0.3 & 0.4\end{array}\end{array}$
a Find the probability distribution of the random variable X Y.
b. Check whether E(XY)=E(X) ' E(Y) by separately evaluating each side of the equality.

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Definitions:

Separated Twins

Twins who have been raised apart from one another, often used in studies to understand the influence of genetics versus environment.

Personalities

The combination of characteristics or qualities that form an individual's distinctive character.

Technical Understanding

The ability to grasp and apply specialized knowledge or skills related to a particular field or technology.

Creative People

Individuals who think outside the box and are able to generate original and innovative ideas or solutions.