(a) The diameter of an ordinary bolt (in mm), X, may be modeled with a Guassian probability density function as ) -

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A The Diameter Of An Ordinary Bolt In Mm X May Be Modeled With A Guassian Probability Density Function As X 0 1 (27.11 KiB) Viewed 122 times

(a) The diameter of an ordinary bolt (in mm), X, may be modeled with a Guassian probability density function as ) -<x<0 in which w and o are the parameters of the distribution. (1) Compute the probability density function of Y, g(y) if the cross-sectional area of a bolt, Y, is equal to X2/4 (6 marks) (1) Compute the expected value of Y, E(Y). (2 marks) Hint: Consider the CDF of the random variable Y, G(y) = P(Y Sy) for (1) E(X)= 1; Var(X)=E[[X-u)*)=rand Var(X)=E(X2)-E?(X) for (ii) (b) A highway engineer invites separate bids for widening five roads. Four contractors submit their quotations. The first contractor is usually successful in getting 55% of similar work in the area, whereas the others have equal chances of 15%. Determine the probability that the first contractor will be given at least four of the jobs on the basis of past performance, (5 marks) n! Hint: [(*1,*z$83,4)= p", ","p."