Probability

SMG2013 Probability Tutorial 2: Random Variables . Determine the value of k so that the following functions can be served as a probability distribution function of the discrete random variable X. f(x) = k[4][4 3 J forx=l, 2, 3, 4 x x Then, nd a. the cumulative distribution function of X. b. the probability of HO 3 X s 2) and P(X > 2) . A box contains ten balls. Three are red and seven are yellow. Three balls are randomly selected. Let X be the red ball. Find the probability mass function of X for both experiments. a. The ball is returned to the box before the next ball is selected (with replacement). b. The ball is not returned to the box and the next ball is selected (without replacement). . Let X have the density function 3x2 ; for01)=% ,nd 49. . The time taken for a student to nish a Statistics test (in hours) has a distribution lnction of the form c(x1)(2x) 1