STATISTICS PROBABILITY DISTRIBUTION PROBLEM

Question

A game is played with an unusual eight-sided die. 

Two faces of the die show a cat, four faces of the die show a dog and the rest of the faces show a snake.  

You roll this unusual die once. If the die shows a cat you get $9, if the die shows a dog you get $3 and if the die shows a snake you lose $20.

Let random variable X be the amount of money you win after rolling this die once.

#1. On your paper, write the probability distribution model for this random variable X (i.e. write down the possible values for the random variable X and the associated probabilities). Type "did it" in blank #1 below.

#2 Use your work in #1 to calculate the expected value for this game played once. Show your work on paper and put your answer in blank #2 below.

#3 Use your work in #1 to calculate the standard deviation for this game played once. Show your work on paper and put your answer in blank #3 below. (round to 2 decimal places if needed)

Answer 1

Let x be the money won

P(x) x x^2 x^2 * P(x)

cat 1/4 9 81 20.25

dog 1/2 3 9 4.5

snake 1/4 -20 400 100

124.75

e(x) = sum of x*P(x) 9*1/4 + 3*1/2 + -20*1/4 = -$1.25

var(x) = sum x^2*P(x) - e(x)^2 = 124.75 - (-1.25)^2 = $123.1875

sd(x) = $11.10