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

question 18

Essay

Let X and Y be two independent random variables with the following probability distributions: $$\begin{array}{l}\begin{array} { l | r r r } x & 1 & 2 & 3 \\\hline p ( x ) & 0.2 & 0.5 & 0.3\end{array}\\\begin{array} { l | r r r } y & - 1 & 0 & 1 \\\hline p ( y ) & 0.3 & 0.3 & 0.4\end{array}\end{array}$$ Find the probability distribution of the random variable X + Y.

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Definitions:

Taste

A sense that allows the detection of flavor, or the aesthetic discernment and appreciation of things.

Hearing

The physiological process by which sound waves are converted into electrical signals that are interpreted by the brain.

Object Permanence

The understanding that objects continue to exist even when they cannot be observed, seen, or heard, a concept important in cognitive development.

Egocentrism

A cognitive trait where an individual cannot fully understand or assume perspectives other than their own.