Question 1

A discrete random variable

X

has the following probability distribution:

P(X=1) = 0.2

,

P(X=2) = 0.5

, and

P(X=5) = 0.3

. What is the mean (expected value) of

X

?

Accepted Answer

2.7

Answer

2.6

Answer

3.0

Answer

2.2

Question 2

Suppose a discrete random variable

X

can take values 0, 10, and 20. If

P(X=1) = 0.2

and

P(X=2) = 0.5

, what is the expected value

P(X=5) = 0.3

?

Accepted Answer

8

Answer

4

Answer

12

Answer

10

Question 3

A game spinner is divided into three sections. It has a

X

probability of landing on 2 points, a

P(X=1) = 0.2

probability of landing on 4 points, and a

P(X=2) = 0.5

probability of landing on 8 points. What is the mean score for a single spin?

Accepted Answer

4

Answer

5

Answer

3.5

Answer

4.6

Question 4

A discrete random variable

X

has the probability distribution where

P(X=1) = 0.2

for

P(X=2) = 0.5

. What is the mean

P(X=5) = 0.3

?

Accepted Answer

3

Answer

2

Answer

3.5

Answer

2.5

Question 5

The probability distribution of a random variable

X

is given by

P(X=1) = 0.2

,

P(X=2) = 0.5

,

P(X=5) = 0.3

, and

X

. Find the mean of

Z

after solving for the constant

c

.

Accepted Answer

1.7

Answer

1.9

Answer

2.1

Answer

1.5

Question 6

A random variable

X

represents the number of heads obtained in two tosses of a fair coin. The probability of getting 0 heads is

P(X=1) = 0.2

, 1 head is

P(X=2) = 0.5

, and 2 heads is

P(X=5) = 0.3

. What is the mean value of

X

?

Accepted Answer

1

Answer

1.5

Answer

0.5

Answer

1.25

Question 7

A discrete random variable

X

represents the profit from a small business venture. There is a

P(X=1) = 0.2

chance of making

P(X=2) = 0.5

, a

P(X=5) = 0.3

chance of making

X

, and a

Z

chance of a loss of

c

(represented as

-100

). What is the mean profit

E(V)

?

Accepted Answer

$170

Answer

$150

Answer

$200

Answer

$230

Question 8

A discrete random variable

X

has the following probability distribution:

P(X=1) = 0.2

,

P(X=2) = 0.5

,

P(X=5) = 0.3

, and

X

. If the mean of

Z

is

c

, what is the value of

-100

?

Accepted Answer

4

Answer

5

Answer

3.5

Answer

6

Question 9

A discrete random variable

X

has a probability distribution where

P(X=1) = 0.2

for

P(X=2) = 0.5

. What is the mean

P(X=5) = 0.3

of this distribution?

Accepted Answer

6

Answer

4

Answer

5

Answer

7.5

Question 10

A discrete random variable

X

can take the values 1, 3, and 5. The probabilities are given by

P(X=1) = 0.2

,

P(X=2) = 0.5

, and

P(X=5) = 0.3

. What is the mean

X

?

Accepted Answer

3.4

Answer

3.0

Answer

3.2

Answer

3.8

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