# Worksheet: Expected Values of Discrete Random Variables

In this worksheet, we will practice calculating the expected value from both a table and a graph and calculating the variance for a probability distribution.

**Q4: **

The frequency table shows the number of cars that 65 families have.

Number of Cars | 1 | 2 | 3 | 4 |
---|---|---|---|---|

Frequency | 10 | 35 | 15 | 5 |

Find the mean number of cars per family.

- A
- B
- C
- D
- E

This data can be expressed as a probability distribution for the discrete random variable as shown. Find the value of , , , and .

1 | 2 | 3 | 4 | |

- A , , ,
- B , , ,
- C , , ,
- D , , ,
- E , , ,

Calculate the expected value of .

- A
- B
- C
- D
- E

**Q15: **

Scarlett had a spinner with ten equal sections labeled with the numbers 1 to 10. She spun it 300 times and recorded the outcomes in a frequency table.

Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|

Frequency | 35 | 27 | 22 | 11 | 24 | 28 | 33 | 35 | 49 | 36 |

If the spinner was fair, how many times would you expect to see each number if you spun it 300 times?

State whether the spinner is biased and why.

- AThe spinner is biased because the numbers did not appear exactly 30 times each.
- BThe spinner is not biased because most of the numbers appeared around 30 times.
- CThe spinner is biased because the number 4 only appeared half as often as expected and the number 9 appeared much more often than expected.

**Q24: **

In an experiment, Emma is going to spin a fair four-sided spinner numbered from 1 to 4. Chloe says that the expected value of the experiment is 2.5. Emma disagrees as she says it is impossible to spin 2.5 and suggests that the expected value is 3. Who is correct and why?

- AEmma is correct because the expected value is the average result of an experiment after a large number of trials, which is 2.5 in this case. However, this is unobtainable on the spinner, so it must be rounded to the nearest whole number, which is 3.
- BChloe is correct because the expected value is the average result of an experiment after a large number of trials, which is 2.5 in this case.

**Q25: **

In an experiment, Hannah rolls two fair six-sided dice and adds the numbers. The probability distribution of the experiment is shown.

2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |

Find the value of , , , and .

- A , , ,
- B , , ,
- C , , ,
- D , , ,
- E , , ,

What is the expected value of the experiment?