Let X and Y have the joint pdf f(x,y)=ce−y,0

Let

X

and

Y

have the joint pdf

f (x, y) = c e^{- y}, 0 < x < 1.2 y, y > 0.

(a) Determine the constant

c

. (b) Find the marginal pdf of

X, f_{X} (x)

P (2 X > 2.2 Y)

. d) Let

ρ_{X Y}

be the correlation coefficient of

X

and

Y

. Let

Z = 2 + X, W = 3 + 3 Y

, and

ρ_{X Y}

be the correlation coefficient between

Z

and

W

. Determine the value of

ρ_{X Y} / ρ_{Z W}

Expert Answer

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A.)

The worth of c is processed by utilizing the property that the amount of all probabilities across the X, Y range is 1. Accordingly, we have here:

∫0∞∫01.2yce−ydxdy=1

∫0∞1.2yce−ydy=1

Applying the item rule of joining, we arrive:

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