An certain brand o upright treezer is available in three ditterent rated capacit

Question

An certain brand o upright treezer is available in three ditterent rated capacities: 16 tt, 18 t, and 20 rt, Let X-the rated capacity of a treezer ot this brand sold at a certain store. 5uppose that X has the tollowing pmt 16 10 20 px) 04 0.50.1 (a) computc )), and Vix ELX) rt (b) if the price of freezer having capacity Xi /UX-02U, what is the expected price paid by the next customer to buy a freezer? (c) What Is the varlance o the prica paid by tha naxt custnmar? (d) suppose that although the rated capacity of freezer is X, the actual capacity s h(X X-U ovx2 what is the expected actual capacity of the freezer purchased by the next customer?

Explanation / Answer

from above :

hence E(X)=17.4

E(X2) =304.4

Var(X)=E(X2)-(E(X))2 =1.64

b)expected price =70E(X)-650 =568

c) variance =702 *Var(X)= 8036

d)expected capacity E(h(x))=E(X)-0.009E(X2) =14.6604

x P(x) xP(x) x2P(x) 16 0.4 6.4 102.4 18 0.5 9 162 20 0.1 2 40 17.4 304.4

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