X \ Y | 0 | 1 | 2 | P[X=x] |
0 | 0.1 | 0.3 | 0.05 | 0.45 |
1 | 0.2 | 0.25 | 0.1 | 0.55 |
P[Y=y] | 0.3 | 0.55 | 0.15 | 1 |
a) P[X= Y] = P[X-Y = 0]
= P[X=0,Y=0]+P[X=1,Y=1 ]
= 0.1 +0.25
= 0.35
b) P[X>Y ] = P[X=1 , Y = 0] = 0.2
c)
So, E[X] = 0.55
So, Var(X) = E[X2] - E2[X] = 0.55 - 0.552 = 0.2475
So, E[Y] = 0.85
So, Var (Y) = 1.15 - 0.852 = 0.4275
d) Again
now,
So, Cov(XY) = 0.45 - 0.550.85 = - 0.0175
and
If you have any doubts, ask me below in the comment section. Thank you
17. From the following joint probability distribution of X and Y,f (a) P(X= Y], P [X...
1. Let the joint probability (mass) function of X and Y be given by the following: Value of X -1 -1 3/8 1/8 Value of Y1 1/8 3/8 (a) Determine the marginal (b) Determine the conditional distribution of X given Y (c) Are they independent? d) Compute E(X), Var(X), E(Y) and Var(Y). (e) Compute PXY <0) and Ptmax(X,Y) > 0 (f) Compute Elmax(X, Y)] and E(XY) (g) Compute Cov(X,Y) and Corr(X, Y) 1
The joint probability density function is f(x, y) for 17. Find the mean of X given Y = random variables X and Y fax, y) = f(xy *** Q<x<10<x<1 Elsewhere w 14. Random variables X and Y have a density function f(x, y). Find the indicated expected value f(x, y) = 6; (xy+y4) 0<x< 1,0<y<1 0 Elsewhere E(x2y) = 15. The means, standard deviations, and covariance for random variables X, Y, and Z are given below. Lex= 3, uy =...
Let the frequency function of the joint distribution of the random variables X and Y P(X = 2, Y = 3) = P(X = 1, Y = 2) = P(X = -1, Y = 1) = P(X = 0, Y = -1) = P(X = -1, Y = -2) = 3 a) Determine the marginal distributions of the random variables X and Y. b) Determine Cov(X,Y) and Corr(X,Y). c) Determine the conditional distributions of the random variable Y as a...
(pts) 1. The joint probability density of X and Y is given by . 0<x<1 and 0 <y<2 otherwise d) Find Cov(X,Y). a) Verify that this is a joint probability density function. b) Find P(x >Y). ) Find Pſy>*<51 c) Find the correlation coefficient of X and Y (Pxy).
Problem 3: X and Y are jointly continuous with joint pdf 0<x<2, 0<y<x+1 f(x,y) = 17 0, Elsewhere a) Find P(X < 1, Y < 2). b) Find marginal pdf's of X. c) f(x|y=1). d) Find E(XY). dulrahim
L UULIOL A (a) Evaluate the conditional distribution K(y/x=1), given the joint probability function f(x,y)= e-*-,x>0,y>0. 4 (bl ynloin the 1 1 :
you have two random variables, X and Y with joint distribution given by the following table: Y=0 | .4 .2 4+.26. So, for example, the probability that Y 0, X - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),f(r). (b) Find the conditional distribution (pmf) of Y give X, denoted f(Y|X). (c) Find the expected values of X and Y, E(X), E(Y). (d) Find the variances of X...
(8pts) 1. The joint probability density of X and Y is given by + 0<x<1 and 0 <y< 2 otherwise a) Verify that this is a joint probability density function. b) Find P(x >Y). o) Find Pſy > for< d) Find Cov(X,Y). e) Find the correlation coefficient of X and Y (Pxy).
1. If the joint probability distribution of X and Y is given by f(x, y) for = 1,2,3; y=0,1,2,3 · 42 2. Referring to Exercise 1, find (a) the marginal distribution of X; (b) the marginal distribution of Y. 3. Referring to Exercises 1 and 2, find (a) The expected value of XY. (b) The expected value of X. (c) The expected value of Y (d) The covariance of X and Y (COV(X, Y)). Round your final answer to 3...
4. Suppose X and Y has joint density f(x, y) = 2 for () < x <y<1. (a) Find P(Y - X > 2). (b) Find the marginal densities of X and Y. (c) Find E(X), E(Y), Var(X), Var(Y), Cov(X,Y)