Find the mean variance and standard deviation of the following probability distribution
Xi: a b
Pi: p q
Where p+q=1.
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