Exercise 12. Seven thousand lottery tickets are sold for $5 each. One ticket will win $2,000, two tickets will win $750 each, and five tickets will win $100 each. Let ? denote the net gain from the purchase of a randomly selected ticket.a. Construct the probability distribution of ?.b. Compute the expected value ?(?) of ?. Interpret its meaning. c. Computer the standard deviation ? of ?.

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Asked Feb 26, 2019
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Exercise 12. Seven thousand lottery tickets are sold for $5 each. One ticket will win $2,000, two tickets will win $750 each, and five tickets will win $100 each. Let ? denote the net gain from the purchase of a randomly selected ticket.

a. Construct the probability distribution of ?.
b. Compute the expected value ?(?) of ?. Interpret its meaning. c. Computer the standard deviation ? of ?.

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Expert Answer

Step 1

Given 

Total lottery tickets sold = 7000

Price of one ticket = $5

number of tickets with prize money $2000 = 1

number of tickets with prize money $750 = 2

number of tickets with prize money $100 = 5

Let X denote the net gain on buying a ticket.

X can take values as shown in  below mentioned table.

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Step 2

Total number of tickets = 7000

number of tickets with prize money $2000 (which gives X = 1995) = 1

P(X=1995) = 1/7000

number of tickets with prize money $750 (which gives X = 745) = 2

P(X=745) = 2/7000

number of tickets with prize money $100 (which gives X = 95) = 5

P(X=95) = 5/7000

number of tickets with prize money $0 (which gives X = -5) = 6992

P(X=-5) = 6992/7000.

Writing all these values of X with respective probabilities we get the probability distribution of X as shown below.

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Step 3

The expected value of a probability distribution is calculated by the below mentioned formula. After substituitng ...

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