An certain brand of upright freezer is available in three different rated capacities: 16 ft3, 18 ft³, 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. 20 16 18 0.3 0.4 0.3 p(x) (a) Compute E(X), E(X2), and V(X). ft3 E(X)= E(X²)= V(x)= (b) If the price of a freezer having capacity X is 64X-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? (Enter your answer to four decimal places.) ft³

The pmf of the amount of memory X (GB) in a purchased flash drive is given as the following. 1 2 4 8 16 p(x) 0.05 0.15 0.30 0.35 0.15 (a) Compute E(X) (in GB). (Enter your answer to two decimal places.) GB (b) Compute V(X) (in GB?) directly from the definition. (Enter your answer to four decimal places.) GB? (c) Compute the standard deviation of X (in GB). (Round your answer to three decimal places.) GB (d) Compute V(X) (in GB?) using the shortcut formula. (Enter your answer to four decimal places.) GB2

Each of the following are composite functions of the form f(g(x)) . Identify the outer function f(x) , the inner function g(x) , and dy dx for each. a. y= 3   1+4x2 f(x)=       g(x)=       dy dx =     b. y=23x2+27x−110 f(x)=       g(x)=       dy dx =     c. y=(33x−1)73 f(x)=       g(x)=       dy dx =

Calculate E(X³), where X has the following PMF: .5 x=1 f(x)=.3 x=2 .2 x=3