One state lottery has 1,100 prizes of $1; 120 prizes of $10; 30 prizes of $50;...
One state lottery has 1,100 prizes of $1; 120 prizes of $10; 30 prizes of $50; 5 prizes of $285; 2 prizes of $1,180; and 1 prize of $2,400. Assume that 34,000 lottery tickets are issued and sold for $1. Round to 4 decimal places for the answers
What is the lottery's expected profit per ticket?
What is the lottery's standard deviation of profit per ticket?
Homework Answers
here X is random variable which denote profit for a random ticket to lettery
| x | f(x) | xP(x) | x2P(x) |
| 0 | 0.032353 | 0.00000 | 0.00000 |
| -9 | 0.003529 | -0.03176 | 0.28588 |
| -49 | 0.000882 | -0.04324 | 2.11853 |
| -284 | 0.000147 | -0.04176 | 11.86118 |
| -1179 | 0.000059 | -0.06935 | 81.76712 |
| -2399 | 0.000029 | -0.07056 | 169.27062 |
| 1 | 0.963000 | 0.96300 | 0.96300 |
| total | 0.7063 | 266.2663 | |
| E(x) =μ= | ΣxP(x) = | 0.7063 | |
| E(x2) = | Σx2P(x) = | 266.2663 | |
| Var(x)=σ2 = | E(x2)-(E(x))2= | 265.7674 | |
| std deviation= | σ= √σ2 = | 16.3024 |
from above:
lottery's expected profit per ticket =0.7063
lottery's standard deviation of profit per ticket =16.3024
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