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:

Protein Synthesis

The biological process by which cells generate new proteins, involving transcription of DNA to mRNA and translation of mRNA to a specific amino acid sequence.

Double Membrane

A double membrane is a structure featuring two lipid bilayers, such as those surrounding certain organelles, including mitochondria and the nucleus in eukaryotic cells.

Eukaryotic Cells

Cells that contain a nucleus enclosed within membranes, distinct from the simpler prokaryotic cells; they include all plant, animal, fungal, and protist cells.

Nucleus

a membrane-bound organelle found in eukaryotic cells that contains most of the cell's genetic material.