Expectation+Prob.+practice+questions

1. The probability distribution of x is given in the table below:

4 || __1__ 4 || __1__ 4 || __1__ 4 || a) Calculate the mean of X b) Calculate the variable of X
 * x || 1 || 2 || 3 || 4 ||
 * P (X=x) || __1__

2. Photo frames are made in a factory. Their widths vary randomly; the widths have a mean of 25cm and variance 3.24. The length of the frames also vary with a mean of 33.5cm and a variance of 5.15. The length of the photo frames are independant of the widths.

a) Calculate the mean difference between the width and the length b) Calculate the variance of the difference between the width and the length

3. The probability distribution of X is given in the table below a) Calculate the mean of X
 * x || 1 || 2 || 3 || 4 || 5 ||
 * P(X=x) || 1/5 || 1/5 || 1/5 || 1/5 || 1/5 ||

b) Calculate the variance of x

4. The result of the mean above (Q3) is multiplied by 8 and added to 3 to give the random variable: L = 8X + 3

a) Calculate E[L]

b) Calculate Var[L]

Answers: 1.a 1.b 2.a 8.5cm 2.b 8.39 (add the variances, never subtract)