Let the RV Y has the pdf
f ( y ) = 6 y ( 1 − y ) , 0 ≤ y ≤ 1 , f ( y ) = 0 elsewhere .
Find E[Y2]
1. Let X be an RV with density f(x) = ¼arosinx + c, x E [-1,11 (f(x) = 0 elsewhere). (a) Compute the constant c. (b) Compute the DF of X. (c) Compute the DF of the RV Y d) Compute P( <0.5) X2.
1. Let X be an RV with density f(x) = ¼arosinx + c, x E [-1,11 (f(x) = 0 elsewhere). (a) Compute the constant c. (b) Compute the DF of X. (c) Compute the DF of...
Let Y be a random variable with PDF F(y) = {(1/2)(1-y) -1≤ y ≤ 1 { 0 elsewhere a) Find the density function of X = 1 - 2Y b) Find the density function of U = Y^2
Let Y be some rv (discrete or continuous). Let the transformation be: U = F (Y ), where F (·) stands for the cdf. Find the pdf of U using the cdf method. Can you name the distribution of U?
1. Let (X, Y) X, Y be two random variables having joint pdf f xy (xy) = 2x ,0 «x « 1,0 « y« 1 = 0, elsewhere. Find the pdf of Z = Xy?
Let Y 1 and Y 2 be defined by the following joint PDF f ( y 1 , y 2 ) = ( 6(1 − y 2 ) 0 < y 1 < y 2 < 1, 0 otherwise (a) (2 pts) Prove that f ( y 1 , y 2 ) is a valid density function. (b) (2 pts) Find the marginal PDF of Y 2 . (c) (2 pts) Use the marginal PDF of Y 2 to find...
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0 < z < i, zero elsewhere, be the pdf of X. (a) Compute E(1/X). (b) Find the edf and the pdf of Y 1/X c) Compute E(Y) and compare this result with the answer obtained in Part (a).
provided that tihe expettauIO 1.8.10. Let f(z) = 2r, 0
10. Let Y1,..., Y, be a random sample from a distribution with pdf 0<y< elsewhere f(x) = { $(0 –» a) Find E(Y). b) Find the method of moments estimator for 8. c) Let X be an estimator of 8. Is it an unbiased estimator? Find the mean square error of X. Show work
1. Let X1 and X2 have the joint pdf f(x1, x2) = 2e-11-22, 0 < 11 < 1 2 < 0o, zero elsewhere. Find the joint pdf of Yı = 2X1 and Y2 = X2 – Xı.
Let the joint pdf of X and Y be , zero elsewhere. Let U = min(X, Y ) and V = max(X, Y ). Find the joint pdf of U and V . 12 (x+y), 0< <1,0 y<1 f (x, y) 12 (x+y), 0
4) (20 pts) Let X be a RV with the following PDF: fx(x) = že=fal for all x. Let Y = X?. (a) Compute E[X]. (b) Find the PDF of Y, fy(y). (c) Compute E[Y].