Notes #4 Probability Distribution Continued!

Mean of a probability distribution: Multiply each outcome by the probability associated with it and find the sum.

 

Example: Rolling a single die

Outcome

1

2

3

4

5

6

Probability

0.17

0.17

0.17

0.17

0.17

0.17

Mean of the distribution: 1(.17) + 2(.17) + 3(.17) + 4(.17) + 5(.17) + 6(.17)= 3.57

 

1. Below is a table that gives the probabilities of obtaining exactly x heads in 4 throws.

x

P(x)

0

.0625

1

.2500

2

.3750

3

.2500

4

.0625

Find the mean:

 

2. Probability Distribution- The weather this weekend

Outcome

Probability

Sunny

80 %

Rain

10 %

Snow

9.99995 %

Volcanic Ash

0.00005 %

The total must equal 100%         Mean can't be calculated with non-number outcomes!


3. Probability Distribution - In Business

Economic Outcome

Probability

Return on Investment

Great

20%

25%

Good

40%

15%

So-So

30%

5%

Really Bad

10%

0%

     Economic Outcome = What might happen next year to the country's overall economy.

     Probability = Estimate of the likelihood that the economy will be in each outcome.

     Return on Investment = Estimate of your profit in each economic outcome.


Find the mean:                                                        What does this mean for Return on Investment?

The mean of a probability distribution is also called the expected value (very important)