# Question: With reference to Example 3 20 find a the marginal distribution

With reference to Example 3.20, find

(a) the marginal distribution function of X, that is, the function given by G(x) = P(X F x) for - ∞ < x < ∞;

(b) the conditional distribution function of X given Y = 1, that is, the function given by F(x| 1) = P(X F x| Y = 1) for - ∞ < x < ∞.

Example 3.20

In Example 3.12 we derived the joint probability distribution of two random variables X and Y, the number of aspirin caplets and the number of sedative caplets included among two caplets drawn at random from a bottle containing three aspirin, two sedative, and four laxative caplets. Find the probability distribution of X alone and that of Y alone.

(a) the marginal distribution function of X, that is, the function given by G(x) = P(X F x) for - ∞ < x < ∞;

(b) the conditional distribution function of X given Y = 1, that is, the function given by F(x| 1) = P(X F x| Y = 1) for - ∞ < x < ∞.

Example 3.20

In Example 3.12 we derived the joint probability distribution of two random variables X and Y, the number of aspirin caplets and the number of sedative caplets included among two caplets drawn at random from a bottle containing three aspirin, two sedative, and four laxative caplets. Find the probability distribution of X alone and that of Y alone.

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