26. Let x represent the number of underinflated tires on  an automobile.  a. Which of the following p(x) functions specifies a  legitimate distribution for x, and why are the other  two not legitimate?   (i) p(0) 5.3, p(1) 5 .2,  p(2) 5 .1, p(3) 5 .05, p(4) 5 .05   (ii) p(0) 5 .4,  p(1) 5 p(2) 5 p(3) 5 .1, p(4) 5 .3 (iii) p(x) 5 .2(3 2 x) for x 5 0, 1, 2, 3, 4  b. For the legitimate distribution of part (a), determine the long-run proportion of cars having at  most two underinflated tires, the proportion having fewer than two underinflated tires, and the  proportion having at least one underinflated tire.

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