Reading Questions 4b | Readings | Introduction to Probability and Statistics | Mathematics

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Problem 1.

Let

X ~

Bernoulli(1/3).

(a) What is $E(X)$ ?

(b) What is $E(X^2)$ ?

Problem 2.

Let

Y ~

binomial(12, 1/3). What is

E(Y)

Problem 3.

Using

X

and

Y

from the previous two problems.

What is $E(4X + 7)$ ?

What is $E(X + Y)$ ?
(Assume $X$ and $Y$ are random variables on the same sample space.)

Problem 4.

The random variable

T

has the following table.

value $a$	-4	-2	0	2	4
pmf $p(a)$	3/10	2/10	1/10	1/10	3/10

(a) Compute $E(T)$ ?

(b) This is the payoff function for a game of chance. The player is paid out the random value in dollars. Negative values means the player loses that much money to the house.

Would you be better off as the player or as the house?

Player
House

Problem 5.

Suppose

W

is a random variable with

E(W) = -1

What is $E(W^2)$ ?

1
-1
Not enough information to say