Answer :

Mean of any probability distribution is given by Mean = ∑xipi

Standard Deviation is given by SD = √ Variance where variance is given by:

Variance = ∑ xi2pi – (∑xipi)2

first we need to find the products i.e. pixi and pixi2 and add them to get mean and apply the above formula to get the variance.

p1x1 = ap and p2x2 = bq Similarly p1x12= a2p and p2x22= b2q

Mean = ap + bq

Variance = a2p + b2q – (ap + bq)2

[ p+q = 1 ……given]


SD = √{pq(a-b)2 } = |a-b|√pq

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