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 /14x^1/2 on the interval [1, 4]