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X2 X1 1 2 3 0.07 0.03 4 0.01 0.01 0.03 0.08 0.01 0.03 0.03 1 0.05 0.02 0.11 О.15 0.01 0.01 3. 0.02 0.07 0.06 0.10 0.03 0.01 4. 0.01 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of X1 given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give EÇX1| X2=3). (g) Give the standard deviation of X1.

X2 X1 1 2 3 0.07 0.03 4 0.01 0.01 0.03 0.08 0.01 0.03 0.03 1 0.05 0.02 0.11 О.15 0.01 0.01 3. 0.02 0.07 0.06 0.10 0.03 0.01 4. 0.01 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of X1 given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give EÇX1| X2=3). (g) Give the standard deviation of X1.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let Xi denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by X2 X1 1 2 3 4. 0.01 0.01 0.03 0.08 0.07 0.03 0.01 1 0.02 0.03 0.03 0.05 2 0.11 О.15 0.01 0.01 0.07 0.06 0.01 3 4 0.02 0.10 0.03 0.01 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of Xı given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give E(X1| X2=3). (g) Give the standard deviation of X1.
Transcribed Image Text:A delivery truck travels from point A to point B and back using the same route each day. There are four traffic lights on the route. Let Xi denote the number of red lights the truck encounters going from A to B and X2 denote the number encountered on the return trip. Data collected over a long period suggest that the joint probability distribution for (X1, X2) is given by X2 X1 1 2 3 4. 0.01 0.01 0.03 0.08 0.07 0.03 0.01 1 0.02 0.03 0.03 0.05 2 0.11 О.15 0.01 0.01 0.07 0.06 0.01 3 4 0.02 0.10 0.03 0.01 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of Xı given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give E(X1| X2=3). (g) Give the standard deviation of X1.
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