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!)

To answer part 1. in each case, integrate and set that equal to ONE.
Then solve for your c.

Quote:

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!)

Please show some effort here.

Part 2 is found using the definition $F(x) = \int_{-\infty}^x f(t) \, dt$ .

Part 3 is basic graphing.

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).

If you need more help then please show what you've done and where exactly you get stuck.