1 What is the variance of the random variable that counts th

1. What is the variance of the random variable that counts the number of 6 that appeared when a fair die is rolled 10 times

2. Provide an example that shows that the variance of the sum of two random variables may not be equal to the sum of variances

Solution

1) The variance of the number of successes in n Bernoulli trials is npq. Here n = 10, p = 1/6 and q = 5/6 . Therefore the variance is 100 /36 = 25 /9 .

2)  Let