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:

Long-Run Average Cost Curve

A curve showing the lowest possible cost at which a firm can produce any given level of output in the long run when all inputs are variable.

Downward Sloping

Describes a line or curve on a graph that shows a decrease in value as it moves from left to right, often used in economics to describe how changes in price affect demand.

Economies of Scale

The cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output decreasing with increasing scale.

Health Insurance Costs

The expenses associated with medical policies that cover the cost of medical services for the insured.