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1 (a) Let f(x) be the probability density function of a continuous random variable X defined...

1 (a) Let f(x) be the probability density function of a continuous random variable X defined by

f(x) = b(1 - x2), -1 < x < 1,

for some constant b. Determine the value of b.

1 (b) Find the distribution function F(x) of X . Enter the value of F(0.5) as the answer to this question.

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