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1. Decide if f(x) = 1/2x2dx on the interval [1, 4] is a probability density function...

1. Decide if f(x) = 1/2x2dx on the interval [1, 4] is a probability density function

2. Decide if f(x) = 1/81x3dx on the interval [0, 3] is a probability density function.

3. Find a value for k such that f(x) = kx on the interval [2, 3] is a probability density function.

4. Let f(x) = 1 /2 e -x/2 on the interval [0, ∞).

a. Show that f(x) is a probability density function

b. . Find P(0 ≤ X ≤ 1)

c. Find P(X ≥ 1)

5. Find the cumulative distribution function for the probability density function

f(x) = 3 /14x1/2 on the interval [1, 4]

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