(a)If you roll a dice five times what is the probability that you will roll more than one 6?

(b)If you roll a dice five times what is the mean and the variance of the number of 6s you will throw? Please use the Binomial formulas (Mean = n.p, Variance = n.p.(1 - p)) to work these out and then check using the general formulas for the mean and variance of any probability distribution:

m = _i P(X _i) and

s² =(X_i - m)²P(X_i)

(c)If you roll a dice five times what is the skewness and the kurtosis of the number of 6s you will throw.

(d)If you roll a 50-sided dice 20 times what is the mean and the variance of the number of 6s you will throw?

(e)Again, rolling your 50-sided dice 20 times, what is the probability of getting three 6s?