W07 - HW Solutions

02

(a)

We know that . Use this to find .

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(b)

The marginal PMF of is given by adding up the rows corresponding to each possible value.

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(c)

(1) Define the possible values of .

Since and , we have that .

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(2) Define PMF of .

Go through each possible value of and see when it occurs.

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(3) Substitute values in for each probability.

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(d)

(1) Find

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(2) Find

03

(1) Compute by summing over .

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(2) Compute by summing over .

05

(a)

(1) Find the marginal PDF for by integrating the joint PDF with respect to .

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(2) Find the marginal PDF for by integrating the joint PDF with respect to .

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(b)

Note that the region of interest is the one above the line . Integrate the PDF over this region.

08

(1) Define and find the CDF of .

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(2) Differentiate to find .

09

	0	1	2
	.25	.5	.25

10

11

(a)

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(b)

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(c)

	0	1	2	3
0	0	0
1	0			0
2			0	0

13

	0.09	0.11	0.05	0.25
	0.17	0.23	0.08	0.48
	0.06	0.15	0.06	0.27
	0.32	0.49	0.19

(a)

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(b)

14

(a)

(1) Write desired probability in terms of values.

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(2) Use lookup table to compute probability.

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(b)

(1) Write desired probability in terms of values.

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(2) Use lookup table to compute probability.

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(c)

(1) Set up conditional probability expression.

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(2) Write desired probability in terms of values.

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(3) Use lookup table to compute probability.