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Problem Set 5

Problem 1 (4.4). Compute E{X} when X is a binomial RV, that is,

Problem 2 (4.5). Let X be a uniform RV, that is,

Compute E{X}.

Problem 3 (4.15). A random sample of 20 households shows the following numbers of children per household: 3, 2, 0, 1, 0, 0, 3, 2, 5, 0, 1, 1, 2, 2, 1, 0, 0, 0, 6, 3. (a) For this set what is the average number of children per household? (b) What is the average number of children in households given that there is at least one child?

Problem 4 (4.19). A particular model of an HDTV is manufactured in three different plants, say, A, B, and C, of the same company. Because the workers at A, B, and C are not equally experienced, the quality of the units differs from plant to plant. The pdf’s of the time-to-failure X, in years, are

where u(x) is the unit step. Plant A produces three times as many units as B, which produces twice as many as C. The TVs are all sent to a central warehouse, intermingled, and shipped to retail stores all around the country. What is the expected lifetime of a unit purchased at random?

Problem 5 (4.21). Compute the variance of X if X is (a) Bernoulli; (b) binomial; (c) Poisson; (d) Gaussian; (e) Rayleigh.

Additional Exercise (if you feel inspired and intrigued)

Problem (Matlab code for the Rolodex problem). Write a Matlab program to evaluate the solution to the “rolodex” problem and plot the average number of calls as a function of the number of students (i.e. re-generate the result of Fig.4.1.-4).