In a single throw of a dice; if `X` denotes the number on its upper face. Find the mean of `X`.

Answer

Mean,`E(X)=1.5`

Explanation

Let `X` denotes the number on its upper face


`therefore X=1,2,3,4,5,6`


Total number of outcomes when throwing a single dice is `6`


`P(X=1)=P(X=2)=P(X=3)=P(X=4)=P(X=5)+P(X=6)=1/6`


Now, Mean, `E(X)=Sigma x_i \ P(x_i)`


`=1 times 1/6+2 times 1/6+3 times 1/6+4 times 1/6+5 times 1/6+6 times 1/6=1/6+2/6+3/6+4/6+5/6+6/6`

`=1/6[1+2+3+4+5+6]=21/6=7/2=3.5`


Thus, Mean,`E(X)=1.5`