Question
Asked Oct 7, 2019
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8. At a raffle, 1500 tickets are sold at $2 each for four prizes of $500, S250, $150, and $75.
You buy one ticket. What are the expected value and the square standard deviation of
your gain?
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8. At a raffle, 1500 tickets are sold at $2 each for four prizes of $500, S250, $150, and $75. You buy one ticket. What are the expected value and the square standard deviation of your gain?

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Expert Answer

Step 1

The gain for each four prizes are given below:

For $500, the gain is $500–$2=$498.

For $250, the gain is $250–$2=$248.

For $150, the gain is $150–$2=$148.

For $75, the gain is $75–$2=$73.

If you loss the game, then the gain is $0–$2=–$2

The probability distribution for the possible gains are tabulated below:

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Gain (x) P(x) $498 Х Р(x) (x-u)^2 (x-)^2*P(x) х-и 499.35 249350.4166.2336 1/1,500 1/1,500 1/1,500 1/1,500 1,496/1,5001.99467 -0.65 0.332 0.165333 249.3562175.42 41.45028 0.098667 149.3522305.42 |14.87028 0.048667 74.35 $248 $148 5527.923 3.685282 $73 -$2 Total 0.4225 0.421373 -1.35 226.6608

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Step 2

The expected gain and the squar...

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E() - ΣΡ (x) =-1.35 Var (x) - σ Σx-μ' P(x) = 226.6608

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