7.3 Exercise 2 — Applied Probability

(See Exercise 6 from "Problems on Random Variables and Probabilities"). A store has eight items for sale. The prices are $3.50, $5.00, $3.50, $7.50, $5.00, $5.00, $3.50, and $7.50, respectively. A customer comes in. She purchases one of the items with probabilities 0.10, 0.15, 0.15, 0.20, 0.10 0.05, 0.10 0.15. The random variable expressing the amount of her purchase may be written

X = 3 . 5 I_{C_{1}} + 5 . 0 I_{C_{2}} + 3 . 5 I_{C_{3}} + 7 . 5 I_{C_{4}} + 5 . 0 I_{C_{5}} + 5 . 0 I_{C_{6}} + 3 . 5 I_{C_{7}} + 7 . 5 I_{C_{8}}

Determine and plot the distribution function for X.

Pfeiffer, Applied Probability, 7.3 Problems on Distribution and Density Functions, exercise 2

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