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...

If F(x1, x2, x3) is the value of the joint distribution function of X1, X2, and X3

Question:

If F(x1, x2, x3) is the value of the joint function of X1, X2, and X3 at (x1, x2, x3), show that the joint marginal function of X1 and X3 is given by
M(x1, x3) = F(x1, ∞, x3) for - ∞ < x1 < ∞,- ∞ < x3 < ∞
And that the marginal 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 function of X1 and X3;
(b) The marginal function of X1.
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...