Question

An certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft², and 20 ft³. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf. 

 (a) Compute E(X), E(X²), and V(X). 

 (b) If the price of a freezer having capacity X is 65X - 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 -0.009x². What is the expected actual capacity of the freezer purchased by the next customer? 

Answer 1

@ Elx) = f'se. P(se) = 1600.3)+ 1810.4) +20 (0.3)+|18|| Elx2) 522 Pc): 162(0.3)+18°(0.4)+902(0,3) = 1326.41 V(De) - Bella Lome ECX 2) - (EX))? 326.4-18= 2.4" Expected price = E(65X-650)= 65 E(X)-650-5201 © V(price)2 V(65%-650) = V(65x) = 652. v(x)= 65x264-101401 ♡ E[h(x)] - E (x-0.009 x) = E(x)-0.009 ECx2)= 18-0.009~326.4 - 575.0624)