Question

If a fair die is thrown 4 times. If x denote the number of throws results in mutiple of 3. Then find mean and variance of x.

Answer 1

Let x be the number of throws results in multiple of 3 is a Binomial variate with n = 4,p = p 

[a die thrown results in multiple of 3] 

= \(\frac{2}{6}\) = \(\frac{1}{3}\)

∴ q =\(\frac{2}{3}\)

Then, mean = np = 4 x \(\frac{1}{3}\)= 1.33.

Variance = npq = 4 x\(\frac{1}{3}\) x\(\frac{2}{3}\) = 0.889.