Discrete Probability and Expected Values

In a certain community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. If a household is selected at random, what is the expected number of children in that household?

• 2.00

• 2.13

• 1.97

• 1.27

A discrete random variable X has the probability distributions shown in the table. Find the value of k.

• 1/3

• 7/12

• 1/12

• 1/4

Determine which of the following distribution is NOT a probability distribution.

• A

• B

• C

• D

A marketing survey compiled data on the number of cars in households.  If X = the number of cars in a randomly selected household, and we omit the rare cases of more than 5 cars, then X has the following probability distribution: 
X           0          1          2          3           4           5    
P(X)   0.24    0.37    0.20    0.11    0.05     0.03
What is the probability that a randomly chosen household has at least two cars?

• 0.20

• 0.29

• 0.39

• 0.61

A stockbroker estimates that at the end of the year, there is a 40% chance a stock will be worth $50, a 35% chance it will be worth $60 and a 25% chance it will be worth $70.
What expected value does this broker assign to this stock's end-of-the-year price?

• $58.50

• $60.00

• $62.50

• $65.00

• A

• B

• C

• D

• A

• B

• C

• D

The prob. distribution represents X= Ana's score on a randomly selected roll when playing Skee Ball. Calculate the expected value E(X).

(a)  

The prob. distribution represents X= Ana's score on a randomly selected Skee Ball roll. Interpret the expected value E(X).

• We expected Ana to score about 23.8 points on any randomly selected Skee Ball roll.

• Ana will score exactly 23.8 points on any Skee Ball roll.

• We expected Ana to score less than 23.8 points on any randomly selected Skee Ball roll.

• We expected Ana to score greater than 23.8 points on any randomly selected Skee Ball roll.

Find the mean (expected value) of the probability distribution.

• 85

• 83.2

• 87.1

• 84.4