Bookmark 1. Based on past experience, an architect detected a probability distri

Question

Bookmark 1. Based on past experience, an architect detected a probability distribution of X, the number of times a drawing must be examined by a client before it is accepted. x p(x) 1 0.1 2 0.2 3 0.3 4 0.2 5 0.2 a) find the average number of times a drawing must be examined by a client before it is accepted b) find the variance of the number of times a drawing must be examined by a client to be accepted c) find the standard deviation of the number of times a drawing must be examined by a client before it is accepted d) what is the probability that a drawing must be examined five times before being accepted e) find the probability that a drawing must be examined at least twice before being accepted f) e) find the probability that a drawing must be examined at most three before being accepted g) e) find the probability that a drawing must be examined less than twice before being accepted

Explanation / Answer

a) Average, E(X) = 1 * 0.1 + 2 * 0.2 + 3 * 0.3 + 4 * 0.2 + 5 * 0.2

                            = 3.2

b) E(X2) = 12 * 0.1 + 22 * 0.2 + 32 * 0.3 + 42 * 0.2 + 52 * 0.2

             = 11.8

Var(X) = E(X2) - (E(X))2

           = 11.8 - 3.22

           = 1.56

c) Stadard deviation = sqrt(1.56) = 1.25

d) P(X = 5) = 0.2

e) P(X > 2) = 1 - [P(X = 1)]

                  = 1 - [0.1]

                  = 0.9

f) P(X < 3) = P(X = 1) + P(X = 2) + P(X = 3)

                 = 0.1 + 0.2 + 0.3

                 = 0.6

g) P(X < 2) = P(X = 1)

                  = 0.1

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