# Question

If E[X] = 1 and Var(X) = 5, find

(a) E[(2 + X)2];

(b) Var(4 + 3X).

(a) E[(2 + X)2];

(b) Var(4 + 3X).

## Answer to relevant Questions

If 10 married couples are randomly seated at a round table, compute (a) The expected number and (b) The variance of the number of wives who are seated next to their husbands. Let X1, . . . be independent with common mean μ and common variance σ2, and set Yn = Xn + Xn+1 + Xn+2. For j ≥ 0, find Cov(Yn, Yn+j). If X1, X2, X3, and X4 are (pairwise) uncorrelated random variables, each having mean 0 and variance 1, compute the correlations of (a) X1 + X2 and X2 + X3; (b) X1 + X2 and X3 + X4. A population is made up of r disjoint subgroups. Let pi denote the proportion of the population that is in subgroup i, i = 1, . . . , r. If the average weight of the members of subgroup i is wi, i = 1, . . . , r, what is the ...Let U1, U2, . . . be a sequence of independent uniform (0, 1) random variables. In Example 5i we showed that, for 0 ≤ x ≤ 1,E[N(x)] = ex, where This problem gives another approach to establishing that result. (a) Show by ...Post your question

0