Download Statistics Notes: 6.1 Probability Distributions

Statistics Notes: 6.1 Probability Distributions
Do you remember?
Create a relative frequency histogram.
6.1 Probability Distributions
Random Variable:
A numerical outcome of a random experiment. denoted X.
Discrete Random Variable:
A countable random variable
Continuous Random Variable:
A measurable random variable
Examples:
• The number of light bulbs in the school that burn out the next year.
• The number of leaves on a randomly selected Oak tree.
• The amount of time between calls to 911.
Probability Distribution:
A distribution of a random variable that gives the outcomes and their probabilities (relative frequencies).
Probability Histogram
A histogram that shows the relationship between the random variable (x) and its probability (y).
Probability Distribution
Probability Histogram
Which of the following are probability distributions? Why?
A.
C.
B.
A Discrete Probability Distribution is:
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Statistics Notes: 6.1 Probability Distributions
The mean of a discrete random variable:
I asked several students the ages of their cars and obtained the following data. 2, 4, 6, 6, 4, 4, 2, 3, 5, 5
Find the average age of the cars.
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2 + 4 + 6 + 6 + 4 + 4 + 2 + 3 + 5 + 5
=
= 4.1
10
10
The formula: =
Mean of a Discrete Random Variable: Multiply the value of each random variable by its probability, then add up the products.
Standard Deviation of a Discrete Random Variable: Suppose a basketball player historically makes 80% of her free throw attempts (free throws are independent). The table below gives the number of successful attempts in 3 shots and the probability of each outcome.
the variance is .48
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Statistics Notes: 6.1 Probability Distributions
Expected Value:
A term life insurance policy will pay a beneficiary a sum of money upon the death of the policy holder. These policies have premiums that must be paid annually. Suppose a life insurance company sells a $250,000 one year term life insurance policy to a 20­year­old male for $350. The probability he will survive the year is 0.99865. Compute the expected value of this policy to the insurance company.
Expected Value: This is the mean of the discrete random variable. Suppose the same life insurance company sells a $250,000 one year term life insurance policy to a 49­year­old female for $520. The probability she will survive the year is 0.99791. Compute the expected value of this policy to the insurance company.
HW: p335 #1 ­ 11 odds, 15, 19, 21, 23
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