# Considered and since the variance is a sum of squared

• 4

This preview shows page 3 - 4 out of 4 pages.

considered. And, since the variance is a sum of squared terms, any multiplier value b must also be squared when adjusting the variance. Example 3: What is the variance if each sum of the number of dots in tossing two dice is multiplied by 2? )
Example 4: The discrete probability distribution of getting a head in tossing two unbiased coins is given below: Number of heads ( x ) 0 1 ( ) P X x = 1 4 1 2 1 4 a. What is the mean number of heads? b. What is the variance number of heads? c. What is the standard deviation number of heads? 2 Solution: 4
Statistics and Probability MODULE III ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 2 2 2 1 1 1 . 0 1 1 1 2 1 4 2 4 1 1 0 4 4 2 4 1 2 b = + + = + + = = 1 . 2 0.707 c =+ = Example 5: Suppose an individual plays a gambling game where it is possible to lose Php 1.00, break even, win Php 3.00, or win Php 5.00 each time he plays. The probability distribution for each outcome is provided by the following table: Outcome -Php 1.00 Php 0.00 Php 3.00 Php 5.00 Probability 0.30 0.40 0.20 What is the mean outcome for this game? 0.10
Example 6: Refer to Example 5, suppose the payout is subtracted Php 1.00 from each prize. The new probability distribution for each outcome is provided by the following table: Outcome -Php 2.00 -Php 1.00 Php 2.00 Php 4.00 Probability 0.30 0.40 0.20 What is the mean outcome for this game? 0.10
• • • 