Find the mean variance and standard deviation of the following probability distribution `x_i : a\ \ b` `p_i : p\ q` Where `p+q=1.`

Answer

Mean`=p(a-b)+b`

Variance`=pq(a-b)^2`

and Standard Deviation`=|a-b| sqrt(pq)`

Explanation

We are given


Mean`=E(X)=Sigma x_i cdot p_i`


`=a times p+ b times `

`=ap+b(1-p) quad quad p+q=1`


`=p(a-b)+b`


`rArr E(X)=p(a-b)+b`


Also,


`E(X^2)= Sigma x^2_i times p_i`


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