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Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 4.3 - Problem 9e
Get Full Access to Probability And Statistical Inference - 9 Edition - Chapter 4.3 - Problem 9e

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# Let X and Y have a uniform distribution on the set of

ISBN: 9780321923271 41

## Solution for problem 9E Chapter 4.3

Probability and Statistical Inference | 9th Edition

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Problem 9E

Let $$X$$ and $$Y$$ have a uniform distribution on the set of points with integer coordinates in $$S=\{(x, y): 0 \leq x \leq$$ $$7, x \leq y \leq x+2\}$$. That is, $$f(x, y)=1 / 24,(x, y) \in S$$, and both $$x$$ and $$y$$ are integers. Find

(a) $$f_{X}(x)$$.

(b) $$h(y \mid x)$$.

(c) $$E(Y \mid x)$$.

(d) $$\sigma_{Y \mid x}^{2}$$.

(e) $$f_{Y}(y)$$.

Equation Transcription:

.

.

.

Text Transcription:

X

Y

S={(x,y):0< or = x < or = 7,x< or = y< or = x+2}

f(x,y)=1/24,(x,y) in S

x

y

f_X(x)

h(y∣x) .

E(Y∣x) .

sigma_Y∣x^2

f_Y (y)

Step-by-Step Solution:

Step 1 of 6 :

Given that X and Y are uniformly distributed with f(x,y)=;0xyx+2 on the set of points on the integer coordinate S={(x,y),0xyx+2}.The given uniform distribution is a discrete uniform distribution, since the set S has only a finite number of outcomes with equal probability.

Step 2 of 6

Step 3 of 6

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