Find the probability distribution of the number of success in two tosses f a die, where a success is defined as getting a number greater than 4. Also, find the mean and variance of the distribution.

Explanation

`P(X=0)=P(F_1).P(F_2)=2/3xx2/3=4/9`
`P(X=1)=P(S_1).P(F_2)+P(F_1)P(S_2)`
`=1/3.(2)/(3)+2/3xx1/3=4/9`
`P(X=2)=P(S_1).P(S_2)`
`=1/3.(1)/(3)=1/9`
The probability distribution is

`Mean =sum_(i=1)^(n)X_iP(x_i)=2/3`
`Var =sum_(i=1)^(n)P_iX_i^2-(sum_(i=1)^(n)P_ix_i)^2=8/9-(2/3)^2=4/9`
Hence, mean `=2/3` and variance `=4/9`