Question: Answer the following: The variable x can have any value in the continuous range 0 g x S 1 with probability density function p(x) =

Answer the following:

The variable x can have any value in the continuous range 0 g x S 1 with probability density function p(x) = 6x(1 x). (a) Derive an expression for the probability, P (x g a), that the value of x is not greater than a. (b) Confirm that p(x) is normalized. (c) Find the mean (x) and standard deviation 0'. (d) Find the probability that (x) 0' g x g (x) + 0

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