# Thread: need help with cdf homework

1. ## need help with cdf homework

For each of the following functions, (1) find the constant, (2) find the c.d.f. F(x), (3) sketch graphs of f(x) and F(x) and (4) find mu and sigma squared.

1. f(x) = x^2/3, 0 < x < c

2. f(x) = (3/16) x^4; -c < x < c

3. f(x) = 1/(cx)^(1/2), 0 < x < 1 (unbounded!)

2. To answer part 1. in each case, integrate and set that equal to ONE.

3. Originally Posted by affelix
For each of the following functions, (1) find the constant, (2) find the c.d.f. F(x), (3) sketch graphs of f(x) and F(x) and (4) find mu and sigma squared.

1. f(x) = x^2/3, 0 < x < c

2. f(x) = (3/16) x^4; -c < x < c

3. f(x) = 1/(cx)^(1/2), 0 < x < 1 (unbounded!)
Part 2 is found using the definition $F(x) = \int_{-\infty}^x f(t) \, dt$.
Part 4 is done using the basic definitions $E(X) = \int_{-\infty} ^{+\infty} x f(x) \, dx$ and $Var(X) = E(X^2) - (E(X))^2$ where $E(X^2) = \int_{-\infty} ^{+\infty} x^2 f(x) \, dx$ (it's assumed that you know how to integrate).