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3. If a dealers profit, in units of $5000, on a new automobile can be looked upon as a random variable X having the den...

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 f

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?
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fa):2Ci-2)if ocac otheswise Avesage proft per automobile:.5000 $1666.7 Variane of x- ECx-E] Standard deviation of x 0-235 0-2e S00 P(K>0-1) 50००) 2(1- O.1 = 0.81 P(x>0)-0.81 A lrobability that profit exceeds $s00 - 081

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