Question

 A computer can generate random numbers which are either 0 or 2. On a particular occasion, it generates a set of numbers which consists of 23 zeros and 17 twos. Find the mean and variance of this set of 40 numbers. 

Answer 1

$$mean=\bar{x}=\dfrac{\sum_ix_i}{n}$$

$$=\dfrac{23(0)+17(2)}{40}=0.85$$

$$Var(X)=\dfrac{\sum_i(x_i-\bar{x})^2}{n}$$

$$Var(X)=\dfrac{23(0-0.85)^2+17(2-0.85)^2}{40}$$

$$=0.9775$$