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Suppose a certain type of small data processing firm is so specialized that some have difficulty...

Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probability density function that characterizes the proportion X that make a profit is given by f(x) A cx^4(1 − x)^2, 0 ≤ x ≤ 1  , 0, eslewherea. Evaluate c that renders f(x) a valid density function. b. Find the probability that at most 50% of the firms make a profit in the first year. d. Find the expectation E[X] and Var(X) of the random variable X.

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