5.02 - Discrete Random Variables

Question 1

Variance of a random variable X

Answer 1

Mean of the squares - square of the mean

Question 2

Expectation of a random variable X

Answer 2

Sum of P(X=x) * X

Question 3

If Y = aX + b then E(Y) =

Answer 3

aE(X) + b

Question 4

If Y = aX +b then Var(Y) =

Answer 4

a^2 Var(X)

Question 5

If X - U(n) then P(X=x) =

Answer 5

1/n for x = 1,2 … n

Question 6

If X - U(n) then E(X) =

Answer 6

(n+1)/2

Question 7

If X - U(n) then Var(X) =

Answer 7

(n^2 - 1)12

Question 8

If x - B(n, p) then E(X) =

Answer 8

np

Question 9

If x - B(n, p) then Var(X) =

Answer 9

np(1-p)

Question 10

What conditions need to be met for geometric.

Answer 10

Constant success probability
Independent trials
All outcomes can be classified as success or failure.
No upper limit to the number of trials.

Question 11

If X - Geo(p) then P(X=x) =

Answer 11

p(1-p)^x-1

Question 12

If X - Geo(p) then E(X) =

Answer 12

1/p

Question 13

If X - Geo(p) then Var(X) =

Answer 13

(1-p)/p^2

Question 14

If X-Po(theta), Y-Po(gamma) and Z = X+Y, then Z -

Answer 14

Po(theta + gamma)

Question 15

What conditions need to be met for poisson.

Answer 15

The events occur randomly.
The events must be independent.
The average rate must be constant.