An certain brand of upright freezer is available in three different rated capaci

Question

An certain brand of upright freezer is available in three different rated capacities: 16 that X has the following pmf , 18 , and 20 ft. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose 16 18 20 p(x) 10.2 0.3 0.5 (a) Compute E(X), E(X2), and V(x) E(X) E(x2) 1t: b) If the price of a freezer having capacity X is 68x- 650, what is the expected price paid by the next customer to buy a freezer? (c) What is the variance of the price paid by the next customer? (d) Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X) = X-0.009x?·What is the expected actual capacity of the freezer purchased by the next customer?

Explanation / Answer

a) E(X) = 16 * 0.2 + 18 * 0.3 + 20 * 0.5 = 18.6

E(X^2) = 16^2 * 0.2 + 18^2 * 0.3 + 20^2 * 0.5 = 348.4

V(X) = E(x^2) - (E(X))^2

        = 348.4 - (18.6)^2

       = 2.44

b) Expected value = 68 * E(X) - 650 = 68 * 18.6 - 650 = 614.8

c) Variance = (68)^2 * V(x) = (68)^2 * 2.44 = 11282.56

d) Expected value = E(X) - 0.009 * E(X^2) = 18.6 - 0.009 * 348.4 = 15.4644

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.