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1. f is a probability density function for the random variable X defined on the given...

1. f is a probability density function for the random variable X defined on the given interval. Find the indicated probabilities.

f(x) = 1/36(9 − x2);  [−3, 3]
(a)    P(−1 ≤ X ≤ 1)(9 − x2);  [−3, 3]

(b)    P(X ≤ 0)

(c)    P(X > −1)

(d)    P(X = 0)

2. Find the value of the constant k such that the function is a probability density function on the indicated interval.

f(x) = kx2;  [0, 3]

k=

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