**Q1: **

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

**Q2: **

The table shows the probability distribution of a fair six-sided die. Determine .

1 | 2 | 3 | 4 | 5 | 6 | |

**Q3: **

The discrete random variable has the shown probability distribution.

1 | 2 | 3 | 4 | 5 | 6 | |

0.1 | 0.3 | 0.2 | 0.1 | 0.1 |

Find the value of .

Hence, determine the expected value of .

**Q4: **

An experiment produces the discrete random variable that has the probability distribution shown. If a very high number of trials were carried out, what would be the likely mean of all the outcomes?

2 | 3 | 4 | 5 | |

0.1 | 0.3 | 0.2 | 0.4 |

**Q5: **

Work out the expected value of the random variable whose probability distribution is shown.

**Q6: **

Work out the expected value of the random variable whose probability distribution is shown.

**Q7: **

Work out the expected value of the random variable whose probability distribution is shown.

**Q8: **

Work out the expected value of the random variable whose probability distribution is shown.

**Q9: **

The function in the given table is a probability function of a discrete random variable . Find the value of .

0 | 1 | 2 | 3 | 4 | |

0.3 | 0.3 |

**Q10: **

The function in the given table is a probability function of a discrete random variable . Find the value of .

0 | 1 | 2 | 3 | ||

0.3 | 0.2 |

**Q11: **

The function in the given table is a probability function of a discrete random variable . Find the expected value of .

1 | 3 | 4 | 6 | |

- A
- B
- C15
- D

**Q12: **

The function in the given table is a probability function of a discrete random variable . Given that the expected value of is 4, find the values of and .

1 | 3 | 5 | 6 | ||

0.2 | 0.2 | 0.2 | 0.3 |

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

**Q13: **

The function in the given table is a probability function of a discrete random variable . Find the value of .

2 | 3 | 4 | 5 | |

- A0
- B
- C
- D

**Q14: **

An experiment that produces the discrete random variable has the probability distribution shown.

2 | 3 | 4 | 5 | |

0.1 | 0.3 | 0.2 | 0.4 |

Calculate .

Calculate .

The variance of can be calculated using the formula . Calculate to 2 decimal places.

**Q15: **

The function in the given table is a probability function of a discrete random variable . Given that the expected value of is 4.8, find the values of and .

1 | 3 | 4 | 5 | ||

0.1 | 0.1 | 0.2 | 0.3 |

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