# need help with cdf homework

• Oct 20th 2009, 10:54 AM
affelix
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!)
• Oct 20th 2009, 02:37 PM
matheagle
To answer part 1. in each case, integrate and set that equal to ONE.
• Oct 20th 2009, 03:41 PM
mr fantastic
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!)

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

Part 3 is basic graphing.

Part 4 is done using the basic definitions $\displaystyle E(X) = \int_{-\infty} ^{+\infty} x f(x) \, dx$ and $\displaystyle Var(X) = E(X^2) - (E(X))^2$ where $\displaystyle E(X^2) = \int_{-\infty} ^{+\infty} x^2 f(x) \, dx$ (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.