Question

In: Statistics and Probability

2. For each of the following joint pmfs nd the value c. a. p(x,y) = c(x...

2. For each of the following joint pmfs nd the value c.

a. p(x,y) = c(x + y), x = 1,2,3, y = 1,...,x

b. p(x,y) = c( 1/4)^x (1/3)^y, x = 0,1,2,..., y = 0,1,2,...

Solutions

Expert Solution

We will use the fact that the sum of all probabilities is 1.

a.

We have,

b.

We have,

orchestra answered 2 years ago
Next > < Previous

Related Solutions

let p ( x , y )be a joint pmf of Xand Y. p ( x...
let p ( x , y )be a joint pmf of Xand Y. p ( x , y ) y = 0 y = 1 y = 2 x = 0 .12 .10 .08 x = 1 .13 .17 .10 x = 2 .15 .15 0 (a) Find the marginal pmf's of Xand Y. (b) Determine whether Xand Yare independent. c) Find Correlation (X,Y)
Consider the following joint distribution. X p(x,y) 2 5 Y 2 0.1 0.34 5 0.31 0.25...
Consider the following joint distribution. X p(x,y) 2 5 Y 2 0.1 0.34 5 0.31 0.25 Based on this distribution, find: E(X) Sd(Y) Corr(X,Y)
Consider the following joint distribution. X p(x,y) 2 4 Y 1 0.11 0.36 6 0.33 0.2...
Consider the following joint distribution. X p(x,y) 2 4 Y 1 0.11 0.36 6 0.33 0.2 Based on this distribution, fill in the blanks below. X p(x,y) 2 4 Y 1 0.11 0.36 6 0.33 0.2 E(X)= Sd(Y)= . Corr(X,Y)=
Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x...
Let the random variable and have the joint pmf X Y f(x,y) = {x(y)^2}/c where x = 1, 2, 3 ; y = 1, 2, x+y<= 4, that is (x,y) are {(1,1), (1,2), (2,1), (2,2), 3,1)} (a) Find . c > 0 (b) Find . μX (c) Find . μY (d) Find . σ2 X (e) Find . σ2 Y (f) Find Cov . (X,Y ) (g) Find p , Corr . (x,y) (h) Are and X and Y independent
1. The joint prob dist of X and Y is given by: P(x,y)=K|x-y|, x=0,1,2, y =...
1. The joint prob dist of X and Y is given by: P(x,y)=K|x-y|, x=0,1,2, y = 1, 2, 3, 4 a) Determine the value of K. b) Determine the marginal distribution of X and hence compute E(X) and Var(X). c) Determine the marginal distribution of Y and hence compute E(Y) and Var(Y). d) Determine E(X|y=3) and Var(Y|y=3). e) Are X and Y independent? 2. The joint prob dist of X and Y is given by: P(x,y) = Kxy, x=1,2,3, 4...
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....
Let the joint pmf of X and Y be defined by f (x, y) = c(x...
Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...
If the joint probability distribution of X and Y f(x, y) = (x + y)/2
If the joint probability distribution of X and Y f(x, y) = (x + y)/2, x=0,1,2,3; y=0,1,2, Compute the following a. P(X≤2,Y =1) b. P(X>2,Y ≤1) c. P(X>Y) d. P(X+Y=4)
The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1)....
The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1). a) Determine the value of C b) Determine the marginal distribution of X and compute E(X) and Var(X) c) Determine the marginal distribution of Y and compute E(Y) and Var(Y) d) Compute the correlation coefficient between X and Y
Let X and Y have joint discrete distribution p(x, y) = 3 20 (.5 x )...
Let X and Y have joint discrete distribution p(x, y) = 3 20 (.5 x ) (.7 y ), x = 0, 1, 2, . . . , and y = 0, 1, 2, . . .. Find the marginal probability function P(X = x). [hint: for a geometric series X∞ n=0 arn with −1 < r < 1, r 6= 0, then X∞ n=0 arn = a 1 − r ]
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT