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

the sum of the lengths of any two sides of a triangle is greater than the length of the third side. if you take the three sides of a triangle and add them in pairs, the sum is greater than (not equal to) the third side. if that is not true, then it is not possible to construct a triangle with the given side lengths.

step-by-step explanation:

(f - g)(x) = 5x^3 - 3

step-by-step explanation:

rearrange these functions vertically, with like terms in separate columns:

f(x) = 5x^3 - 2

g(x) =         +1

now subtract, column by column:

(f - g)(x) = 5x^3 - 3