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# 26. Let x represent the number of underinflated tires on an automobile. (a) Which of the following p(x) functions specifies a legitimate distribution...

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) = 0.3, p(1) = 0.2,  p(2) = 0.1, p(3) = 0.05, p(4) = 0.05

(ii) p(0) = 0.4, p(1) = p(2) = p(3) = 0.1, p(4) = 0.3

(iii) p(x) = 0.2(3-x) for x = 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 of cars having fewer than two underinflated tires, and the proportion having at least one underinflated tire.

(a) For a legitimate distribution for x , it must satisfy the following conditions. 1) p(x) ﻿ ≥ ﻿ 0 2) ﻿ ∑ ﻿ p(x)... View the full answer

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