Abox contains three cards, labeled 1, 2, and 3. two cards are chosen at random, with the first card being replaced before the second card is drawn. let x represent the number on the first card, and let y represent the number on the second card.

a. find the joint probability mass function of x and y.
b. find the marginal probability mass functions px(x) and py(y).
c. find µx and µy.
d. find µxy.
e. find cov(x, y).

Step-by-step explanation:

Given that a box ontains three cards, labeled 1, 2, and 3.

Two cards are chosen at random, with the first card being replaced before the second card is drawn.

Let X represent the number on the first card, and let Y represent the number on the second card.

Since drawing is done with replacement, we find that X and Y are independnet

A) Joint pdf of x and y are

y    x0123Total

00.06250.06250.06250.06250.25

10.06250.06250.06250.06250.25

20.06250.06250.06250.06250.25

30.06250.06250.06250.06250.25

Total0.250.250.250.25  

B) Pdf of X is

x        0     1       2       3

p    0.25  0.25 0.25 0.25

and Y also will have same pdf

C)

D)

E) Cov (x,y) =0 since X and Y are independent

6 meters

step-by-step explanation: