Answer to Question #152025 in Statistics and Probability for JG

Question

A survey was conducted among some first graders and one of the questions was how much money they spent on their school cafeteria. The random variable x represents the amount of money spent on a particular day with the corresponding probability P(X).

x 1 3 5 10 20
P(X) 0.16 ? 0.22 0.22 0.08


a) What is the probability that a 1st grader spends exactly 3 dollars?
b) Calculate the expected value, variance, and standard deviation of the random variable X?

Answer 1

Solution:

a).

$P(X=3)= 1-(0.16+0.22+0.22+0.08)$ $=0.32$

b).

$E(X) = \sum xP(X=x)$

=1(0.16)+3(0.32)+5(0.22)+10(0.22)+20(0.08)

$=6.02$

$Var(x) = \sum x^2 P(x) - {(E(x))} ^2$

$=1^2(0.16)+3^2(0.32)+5^2(0.22)$

$+10(0.22)+20(0.08)$

$=62.54- {(6.02)}^2$

= 26.2996

Standard deviation

$Sd = \sqrt {var}$

$= \sqrt {26.2996} =5.1283$