Question

While playing Monopoly, Robin estimated the probabilities of the non-zero rents according to the following probability distribution:

x $2 $14 $20 $100
P(x) 0.40 0.20 0.20 0.20

Consider the random variable x = dollar amount in rent in a Monopoly roll.

a. If the table above specifies the probability distribution f(x), what is the mean of the random variable x?
b. If the probabilities are associated with the outcomes as in the table above, what is the standard deviation of the random variable x?

Answer 1

Explanation:

Given the data table :

x : __ $2_ $14_ _$20 __ $100

P(x) : 0.40_ 0.20 _0.20 _0.20

The mean :

E(x) = Σ(x*p(x))

E(x) = (2*0.4) + (14*0.2) + (20*0.2) + (100*0.2)

E(x) = 27.6

The standard deviation :

SD(x) = sqrt(Σ(x² * p(x)) - E(x)²)

Σ(x² * p(x)) - E(x)² :

((2^2*0.4) + (14^2*0.2) + (20^2*0.2) + (100^2*0.2)) - 27.6^2

2120.8 - 761.76

= 1359.04

Sqrt(1359.04)

SD(x) = 36.865159

SD(x) = 36.87