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

$\mu=\sum x* P(x)=-10*0.5+1*0.25+3*0.15+10*0.09+20*0.01=-3.2$

σ² = (0.5×(-10--3.2)²+0.25×(1--3.2)²+0.15×(3--3.2)²+0.09×(10--3.2)²+0.01×(20--3.2)²) / (0.5+0.25+0.15+0.09+0.01) = 54.36

σ=$\sqrt{σ^2}=7.37$