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

question 49

Essay

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

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Definitions:

Personal Goals

Individual objectives or ambitions that a person aims to achieve.

Group Goals

Objectives or targets collectively set by a group to be achieved through collaborative effort.

Conformity

The act of adjusting one's behavior or thinking to match those of other people or to fit into societal norms.

Group Judgment

The collective decision-making process or opinion-forming within a group, which may be influenced by group dynamics, conformity, and persuasion techniques.