An electronics company manufactures 3 models of microprocessors. The models sell for the following prices: Model A: $20, Model B: $40 and Model C: $60. Customers buying microprocessors from this company choose the various models with the following probabilities: P(A) = 0.2, P(B) = 0.7, P(C) = 0.1.

(a) A market analyst wishes to calculate the average price of chips that customers purchase. Calculate this average or mean price. (b) The plot below shows the probability density function f(x) for the maximum sustainable clock speed of the model A microprocessor.

Find the mean of the maximum sustainable clock speed for the model A microprocessor. (c) Find the cumulative distribution function F(x) for this random variable. (d) Compute the probability that the maximum sustainable clock speed for a model A will be less than 60 kHz. (e) Compute the probability that the maximum sustainable clock speed for a model A will be between 60 and 80 kHz.

f(x) 1/40 20 40 60 80 100 120 x (kHz)