A fair die is tossed. Let `X` denote 1 or 3 according as an odd or an even number appears. Find the probability distribution, means variance of `X`.

Answer

Mean, `E(X)=5` and Variance, `var(X)=1`

Explanation

When a fair dice is thrown there is only 6 total possible outcomes


Let `X` denote `1 "or" 3` according as an odd or an even number appears.


`therefore X` can take values `1,3`

`1` for dd number appear and `3` for even number

Now the probability of drawing the number appears on the dice:


`For P(X=1),`

The outcomes for odd number by drawing a dice is `{1,3,5}=3`


So, `P(X=1)=3/6=1/2`


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