B2. Let X and Y be two continuous random variables with joint density function S ca*y, if 0

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B2. Let X and Y be two continuous random variables with joint density function
S cr*y, if 0 <y SI<1,
fx.x(x, y)
1 0,
otherwise.
(a) Find the value of constant c.
(b) Find the marginal density functions fx(x) and fy (y). Are X and Y independent?
why/why not?
(c) Find the conditional density fyx=z(y|x), use this to compute E[Y|X], and show
that E[E[Y|X]] = E[Y].
(d) Find P(Y <).
Transcribed Image Text:B2. Let X and Y be two continuous random variables with joint density function S cr*y, if 0 <y SI<1, fx.x(x, y) 1 0, otherwise. (a) Find the value of constant c. (b) Find the marginal density functions fx(x) and fy (y). Are X and Y independent? why/why not? (c) Find the conditional density fyx=z(y|x), use this to compute E[Y|X], and show that E[E[Y|X]] = E[Y]. (d) Find P(Y <).
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