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th h. 1. Let the random variables(hand the values equiprobably. Let rhx (a) Find the probability density function (P...
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry,...
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry, where 0 < y < z < 2. (a) Find the value of c that makes fx.y (a, y) a valid pdf. (b) Calculate the marginal density functions for X and Y (c) Find the conditional density function of Y X (d) Calculate E(X) and EYIX) (e Show whether X. Y are independent or not.
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
P7 continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The...
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
1. a) Let X and Y be random variables with the following joint probability density function...
1. a) Let X and Y be random variables with the following joint probability density function (pdf) Зу f(x,y) = 0<y< 2x2,0<x< 1. 2.02 i) Obtain the value for E(Y|X = }). ii) Show the relationship between E[Y|X] and E[XY]. Use this result to obtain E[XY]
1 (10pts) Let U1, U2, ... ,Un be independent uniform random variables over [0, 0] with...
1 (10pts) Let U1, U2, ... ,Un be independent uniform random variables over [0, 0] with the probability density function (p.d.f). () = a 2 + [0, 03, 0 > 0. Let U(1), U(2), .-. ,U(n) be the order statistics. Also let X = U(1)/U(n) and Y = U(n)- (a) (5pts) Find the joint probability density function of (X, Y). (b) (5pts) From part (a), show that X and Y are independent variables.
(1 point) 3. Let X and Y be random variables with a joint probability density function...
(1 point) 3. Let X and Y be random variables with a joint probability density function f(z, y)e (a)Find the marginal distribution functions of X and Y, respectively. i.e. Find f(z) and f(y) f(x)- elsewhere (b) Identify the distribution of Y. What is the E(Y) and SD(Y) E(Y)- (c) Are X and Y independent random variables? Show why, or why not (d) Find P(1 X 2|Y 1) E SD(Y)-
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density...
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
2. Suppose that Y and Y2 are continuous random variables with the joint probability density function...
2. Suppose that Y and Y2 are continuous random variables with the joint probability density function (joint pdf) a) Find k so that this is a proper joint pdf. b) Find the joint cumulative distribution function (joint cdf), FV1,y2)-POİ уг). Be y, sure it is completely specified! c) Find P(, 0.5% 0.25). d) Find P (n 292). e) Find EDY/ . f) Find the marginal distributions fiv,) and f2(/2). g) Find EM] and E[y]. h) Find the covariance between Y1...
Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z...
Let Ņ, X1. X2, . . . random variables over a probability space It is assumed that N takes nonnegative inteqer values. Let Zmax [X1, -. .XN! and W-min\X1,... ,XN Find the distribution function of Z and W, if it suppose N, X1, X2, are independent random variables and X,, have the same distribution function, F, and a) N-1 is a geometric random variable with parameter p (P(N-k), (k 1,2,.)) b) V - 1 is a Poisson random variable with...
Let the random variables X, Y with joint probability density function (pdf) fxy(z, y) = cry, where 0 < y < z < 2. (a) Find the value of c that makes fx.y (a, y) a valid pdf. (b) Calculate the marginal density functions for X and Y (c) Find the conditional density function of Y X (d) Calculate E(X) and EYIX) (e Show whether X. Y are independent or not.
. Let X and Y be the proportion of two random variables with joint probability density function f(r, y) e-*, 0, if, 0 < y < x < oo, elsewhere. a) Find P(Xc3.y-2). b) Are X and Y independent? Why? c) Find E(Y/X)
P7
continuous random variable X has the probability density function fx(x) = 2/9 if P.5 The absolutely continuous random 0<r<3 and 0 elsewhere). Let (1 - if 0<x< 1, g(x) = (- 1)3 if 1<x<3, elsewhere. Calculate the pdf of Y = 9(X). P. 6 The absolutely continuous random variables X and Y have the joint probability density function fx.ya, y) = 1/(x?y?) if x > 1,y > 1 (and 0 elsewhere). Calculate the joint pdf of U = XY...
1. a) Let X and Y be random variables with the following joint probability density function (pdf) Зу f(x,y) = 0<y< 2x2,0<x< 1. 2.02 i) Obtain the value for E(Y|X = }). ii) Show the relationship between E[Y|X] and E[XY]. Use this result to obtain E[XY]
1 (10pts) Let U1, U2, ... ,Un be independent uniform random variables over [0, 0] with the probability density function (p.d.f). () = a 2 + [0, 03, 0 > 0. Let U(1), U(2), .-. ,U(n) be the order statistics. Also let X = U(1)/U(n) and Y = U(n)- (a) (5pts) Find the joint probability density function of (X, Y). (b) (5pts) From part (a), show that X and Y are independent variables.
(1 point) 3. Let X and Y be random variables with a joint probability density function f(z, y)e (a)Find the marginal distribution functions of X and Y, respectively. i.e. Find f(z) and f(y) f(x)- elsewhere (b) Identify the distribution of Y. What is the E(Y) and SD(Y) E(Y)- (c) Are X and Y independent random variables? Show why, or why not (d) Find P(1 X 2|Y 1) E SD(Y)-
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
. Let X and Y be the proportion of two random variables with joint probability density function f(x, y)o, elsewhere. (a) Find P(X < 3|Y= 2). (b) Are X and Y independent? Why? (c) Find E(Y/X)
2. Suppose that Y and Y2 are continuous random variables with the joint probability density function (joint pdf) a) Find k so that this is a proper joint pdf. b) Find the joint cumulative distribution function (joint cdf), FV1,y2)-POİ уг). Be y, sure it is completely specified! c) Find P(, 0.5% 0.25). d) Find P (n 292). e) Find EDY/ . f) Find the marginal distributions fiv,) and f2(/2). g) Find EM] and E[y]. h) Find the covariance between Y1...
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