2. Let X be a random variable with the following pmf: x-969 f(x) 1/6 ½ 1/3 What

Question

2. Let X be a random variable with the following pmf: x-969 f(x) 1/6 ½ 1/3 What is E[2K + 1 ? Let X be a random variable with probability mass function f(x) = (x2+4)/ 30, x= 0, 1, 2, 3. (a) Find E 8. (b) Find Var (X) 4. Let X be a random variable with E(X) = 5 and E [x(X-1)]-27.5. What is Var ? 5. Suppose a school has 20 classes: 16 with 25 students in each; 3 with 100 students in each; and 1 with 300 students (1000 students in all). (a) What is the average class size? (b) Select a student randomly from the 1000 students. Let the random variable X be the size of the class to which the student belongs. Define the p.m.f. of X. (c) What is E(X

Explanation / Answer

Ans:

2)E(X)=-3*(1/6)+6*(1/2)+9*(1/3)

=-0.5+3+3

=5.5

E(X2]=9*(1/6)+36*(1/2)+81*(1/3)=1.5+18+27=46.5

E[(2X+1)2]=E[4X2+1+4X]=4*E[X2]+1+4*E[X]=4*46.5+1+4*5.5=186+1+22=209

4)E[X(X-1)]=E[X2-X]=E[X2]-E[X]=27.5

E[X2]=27.5+5=32.5

Var(X)=E[X2]-E[X]2=32.5-25=7.5

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