# Question

If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal distribution function of X1 and X3 is given by

M(x1, x3) = F(x1, ∞, x3) for - ∞ < x1 < ∞,- ∞ < x3 < ∞

And that the marginal distribution function of X1 is given by

G(x1) = F(x1, ∞, ∞) for - ∞ < x1 < ∞

With reference to Example 3.19, use these results to find

(a) The joint marginal distribution function of X1 and X3;

(b) The marginal distribution function of X1.

M(x1, x3) = F(x1, ∞, x3) for - ∞ < x1 < ∞,- ∞ < x3 < ∞

And that the marginal distribution function of X1 is given by

G(x1) = F(x1, ∞, ∞) for - ∞ < x1 < ∞

With reference to Example 3.19, use these results to find

(a) The joint marginal distribution function of X1 and X3;

(b) The marginal distribution function of X1.

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