**Discrete Random Variables**** **

**Key Concepts:**

** ** |
**Discrete** |
**Continuous** |

**Data recorded by…** |
**Counting** |
**Measuring** |

**values for ‘x’** |
**Whole #** |
**Any real #** |

**Question?** |
**How many?** |
**How long? /heavy?** |

**Probability Question?** |
**P(x = 4)** |
**P(3 < x < 5) ** |

**Expected value:**** symbol = E(x)**
- E
**xpected value = E(x) ****= ***μ*

**Applications of E(x)**** **

#### A raffle has 400 tickets and has a first prize of $500, second prize of $200 and a third prize of $80. Prizewinners are drawn, without replacement, in order First consider $5 a ticket then $2 a ticket.

#### (1^{st}, 2^{nd}, 3^{rd}).

#### Let X be a random variable representing the winnings of a single ticket buyer.

#### Insurance

#### A house insured at a value of $240 000 has the probability of burning down estimated to be 0.0008 per year.

#### What should the insurance company charge for a premium if it wants to make an average profit of $240 per house per year that it is insured?

#### Let X be a random variable representing the amount that the company has to pay out.