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

question 36

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 XY.
b. Check whether E(XY) = E(X) ´ E(Y) by separately evaluating each side of the equality.

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Definitions:

Pyroclastic Material

Fragmented material ejected during volcanic eruptions, including ash, bomb, lapilli, and volcanic blocks, which varies in size, shape, and composition.

Mudflows

Rapid downhill movement of water-laden earth materials, primarily composed of fine-grained soils and clays, which can cause significant erosion and damage.

Pyroclastic Flow

A hot, fast-moving and deadly mixture of gases, ash, and volcanic material produced by explosive eruptions.

Scoria

A highly vesicular, dark colored volcanic rock that may or may not contain crystals, typically formed from the cooling of lava.