The function f (x) = kxⁿ (1 - x)^m, 0 ≤ x ≤ 1 where n > 0, m > 0, and k is a constant, can be used to represent various probability distributions. If k is chosen such thatthen the probability that x will fall between a and b (0 ≤ a ≤ b ≤ 1) isThe probability that a person will remember between 100a% and 100b% of material learned in an experiment is

where x represents the proportion remembered. (See figure.)

(a) For a randomly chosen individual, what is the probability that he or she will recall between 50% and 75% of the material?(b) What is the median percent recall? That is, for what value of b is it true that the probability of recalling 0 to b is 0.5?

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S₁ f(x) dx = 1