Find the probability distribution of the maximum of two scores obtained when a die is thrown twice. Determine also the mean of the distribution.

Explanation

Let X is the random variable score obtained when a die is thrown twice.
`therefore X=1,2,3,4,5,6`
Here, S={(1,1),(1,2),(2,1),(2,2),(1,3),(2,3),(3,1),(3,2),(3,3),…..,(6,6)}
`therefore P(X=1)=1/6cdot1/6=1/36`
`P(X=2)=1/6cdot1/6+1/6cdot1/6+1/6cdot1/6=3/36`
`P(X=3)=1/6cdot1/6+1/6cdot1/6+1/6cdot1/6+1/6cdot1/6+1/6cdot1/6=5/36`
Similarly, `P(X=4)=7/36`
`P(X=5)=9/36`
`P(X=6)=11/36`
So, the required distribution is,

Also, we know that, Mean `{E(X)}=sumXP(X)`
`=1/36+6/36+15/36+28/36+45/36+66/36=161/36`