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:

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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 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.