Question

The following probability model gives the probability structure of a lottery ticket sold in Florida.
X -$10 $1 $3 $10 $20
P(X) 0.5 0.25 0.15 0.09 0.01


Calculate the mean, variance, and standard deviation.

Answer 1

Mean =$\sum X. P(X)$

=(-10*0.5)+(1*0.25)+(3*0.15)+...+(20*0.01)

=-3.2

Variance =$\sum X^2 P(X) - \mu ^2$

$=((-10^2*0.5)+(1^2*0.25)+...+(20^2*0.01))-(-3.2^2)$

=14.36

Standard deviation =$\sqrt {variance}$

=$\sqrt {14.36}$

=3.879