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HW on independent rivins I - © Let sa o<x<1 - ocy<x</ f(x,y)= z ó otherwise...
6. Let f(x,y) = 1 if 0 < y < 2x, 0<x<1, and 0 otherwise. Find the following: a) f(y|x) b) E(Y|X = x) c) The correlation coefficient, p, between X and Y
2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0 < y < 2, f(z,y) (a) [6 pts] Determine if X and Y are independent. (b) [6 pts] Find P{X+Y <1) B( (c) [6 pts) Find 2. Let the joint probability density function of (X, Y) be given by {ay otherwise. 1 and 0
please explain each step 5.21 Let X and Y be independent random variables with fae-ax, x>0 fx(x) = 10. otherwise and Be-Bt, x>0 fr(y) = 10 otherwise where a and B are assumed to be positive constants. Find the PDF of X + Y and treat the special case a = B separately.
Let (X,Y) have joint pdf given by f(x, y) = { Sey, 0 < x <y<, | 0, 0.W., (a) Find the correlation coefficient px,y (b) Are X and Y independent? Explain why.
5. Let ffx)= cx for 1 < x< c0, zero otherwise be the pdf for the random variable X. a) Find c b) Find F(x). c) Find P(X> 3.2). d) Find E(X).
5. Let the joint probability density function of X and Y be given by, f(x,y) = 0 otherwise (a) Find the value of A that makes f (x, y) a proper probability density function (b) Calculate the correlation coefficient of X and Y. (c) Are X and Y independent? Why or why not?
Extra: Let X, Y, Z be results of three independent tosses of a fair die. (a) Find the covariance of the random variables W=2X-3Y + Z (b) Find the correlation coefficient of W and V. and V=X-2Y-Z
Let X and Y be continuous random variables with following joint pdf f(x, y): y 0<1 and 0<y< 1 0 otherwise f(x,y) = Using the distribution method, find the pdf of Z = XY.
Let (X,Y) have joint pdf given by sey, 0 < x < y < 0, f(x, y) = { ( 0, 0.W., (a) Find the correlation coefficient px,y: (20 pts) (b) Are X and Y independent? Explain why. (10 pts)
Let f(x,y) = cx( 1-y), 0 < x < 2y < 1, zero elsewhere. a) Find c. b) Are X and Y independent? Why or why not? c) Find PX +Y05)