x has a distribution which is partly continuous and partly discrete. x has a discrete point of probability at X=1 with probability p, where 0<p<1

on the interval (0,1) X has a constant density of (1-p)/2,

and on the interval (1,2) X has constant density of (1-p)/2

find the variance of X in terms of P . The answer is (2-p)/3

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