Tutorial 4, Q1,2,3,4 thanks

11:22 PM Mon 6 Sep 1 31% + : 0 X Nanyang Technological University SPMS/Division of Mathematical Sciences MH2814 Probability & Statistics Tutorial 4 Topics: Probability density distribution functions, Cumulative distribution functions; Expectation or Expected value. . . . . . . . . . . . . . . . . . . . 1. The proportion of people who respond to a certain mail-order solicitation is a contin- uous random variable X that has the density function f ( 2 ) =105 2 ( +2), 0 0 , elsewere. (a) Evaluate P(X > 2). (b) Find the probability density function of X. 4. Suppose that an antique jewelry dealer is interested in purchasing a gold necklace for which the probabilities are 0.22, 0.36, 0.28, and 0.14, respectively, that she will be able to sell it for a profit of $ 250, sell it for a profit of $ 150, break even, or sell it for a N I - loss of $ 150. What is her expected profit? (+