Question

3. If a dealers profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the density function f(x) = 2(1 - ), o if 0<x<1, elsewhere. (a) Find the average profit per automobile. (b) Find the standard deviation ox. (c) Find the variance of the dealers profit. (d) Demonstrate that Chebyshevs theorem holds for k = 2 with the density function above (e) What is the probability that the profit exceeds $500?

Answer 1

fa):2Ci-2)if ocac otheswise Avesage proft per automobile:.5000 $1666.7 Variane of x- ECx-E] Standard deviation of x 0-235 0-235? ^S000= $1l?8.5 . Standard deviation of profit dealers protit.s 000. so00 - $1,383,8tt6.9 9Variane of dChebyshev's theorem P(-ksx<tke)2 1 Given ke2 P(농-2x0.2357 <Ac+2리 0.2352) 2 1-t 4 0-8043 2C1-2) d2 23 4 O.9619 20.9S Chebyshev's theorem holds for x

e S00 P(K>0-1) 50००) 2(1- O.1 = 0.81 P(x>0)-0.81 A lrobability that profit exceeds $s00 - 081

Answer 2

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Answer 3

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