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Statistics and Probability Chapter 16 Guided Notes Name ________________________________ Date _________________ Period __________

****Read the Introduction on page 342 and the blue box “What is an Actuary?” on page 343.****

________________

**Variable**

- _________________ value based upon the outcome of a ____________ event. ______________ letters, like _____, are used to denote random variables. Any particular value, such as 5, that a random variable can have will be denoted by a ______________________ letter. _________________

**Model**

– the collection of all the possible _________ and the _________________ that they occur for the random variable. o

**Example A**

: Suppose that the death rate in any one year for an insurance company is 1 out of every 1000 people that another 2 out of 1000 suffer some kind of disability and everybody else didn’t require the use of either type of insurance. The probability model for this scenario can be displayed in a table.

**Policyholder Outcome**

*X = Payout *

**Probability P( X) **

Death

*x = *

Disability

*x = *

**__________________ _____________ - **

the theoretical long-run average value of a random variable. It is the _____________ of the probability model. The expected value is denoted by ______ or ________. It is found by __________________ the ______________ of variable values and __________________.

o

**Example B:**

On average, what can the insurance company in the problem above expected to payout per policy? Is the company making a profit if they charge only $50 per year for this benefit?

o o

**Example B, Part 2: **

The expected value can be calculated second way by multiplying each payout by the probability that it occurs!

**Explain what this value means in context! Example C:**

Someone had to take his minivan in for repair because the air-conditioner was cutting out intermittently. The mechanic identified the problem as dirt in a control unit. The mechanic said that in about 75% of such cases, drawing down and then recharging the coolant a couple of times cleans up the problem – and costs only $60. If that fails, then the control unit must be replaced at an additional $100 for parts and $40 for labor.

Define the random variable and construct the probability model.

What is the expected value of the cost of this repair?

What does this value mean in this context?