Concepts of Probability Theory by Paul E. Pfeiffer

Author:Paul E. Pfeiffer
Language: eng
Format: epub, azw3
Publisher: Dover Publications, Inc.
Published: 2013-06-26T16:00:00+00:00

have the following values:

If t1 = −1, t2 = 1, t3 = 2, u1 = −2, u2 = 2, plot the joint distribution function FXY(t, u) by giving the values in each appropriate region of the t, u plane.

3-23. Let X(·) and Y(·) be two discrete random variables. X(·) has range ti = i − 3, i = 1, 2, 3, 4, 5, and Y(·) has range uj = j − 1 for j = 1, 2, 3. Values of the joint probabilities p(i, j) are given as follows:

(a) Determine the marginal probabilities, and show the joint and marginal mass distributions on the plane and on the coordinate lines.

(b) Show values of the joint distribution function FXY(t, u) by indicating values on the appropriate regions of the plane.

3-24. Two random variables X(·) and Y(·) are said to have a joint gaussian (or normal) distribution iffi the joint density function is of the form

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