Use the Definition for the Conditional Distribution of Y Given

question 10

Essay

Use the definition for the conditional distribution of Y given X = x and the marginal distribution of X to derive the formula for Pr(X = x, Y = y). This is called the multiplication rule. Use it to derive the probability for drawing two aces randomly from a deck of cards (no joker), where you do not replace the card after the first draw. Next, generalizing the multiplication rule and assuming independence, find the probability of having four girls in a family with four children.

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Definitions:

Epiglottis

A leaf-shaped flap of cartilage located behind the tongue, at the top of the larynx, which prevents food from entering the airways during swallowing.

Uvula

A small, fleshy extension at the back of the soft palate that hangs above the throat, playing roles in speech and preventing food from entering the nasal cavity.

Innervated

Supplied with nerves; refers to organs or tissues that have nerve fibers connected to them.