# Statistics question Continous Random Variables

## Homework Statement

1) Let X have the p.d.f f(x) = 3(1-x)2, 0≤x<1. Compute:

a) P(0.1 < X < 0.5)

etc...

2) Find the mean and variance, and determine the 90th percentile , of each of the distributions given by the following densities:

a) f(x) 2x, 0≤0<0
etc..

3) Find the 50th percentile ( median ), the 25th percentile ( first quartile ), the 75th percentile ( third quartile ), and the 90th percentile ( also called the ninth decile ) for the following densities:

a)4x3 , 0≤x<1
etc..

Consider the uniform ( rectangular ) distribution on the space [a,b), where a<b, with p.d.f

f(x) 1/b-a' a≤x<b

a) Obtain the cumulative distribution function F(x). Determine the median and the first and third quartiles, and calculate the mean and variance.

I really just need to know which formulas I use here. The book has several pages deriving formulas, I can't see the wood for the trees. Related Calculus and Beyond Homework Help News on Phys.org
You shouldn't need too many formulas, especially not for the first question. What is the definition of a pdf? What are the definitions of mean, variance, quartiles, and cdf? Show us some of your work so we can help.

What you mean? I don't know how to start/do it. Those are all different problems. And I don't know how to calculate the mean and variance for one number ( one you plug in the number for the x ). That must be the mean, then. And you mean the formula for p.d.f and c.d.f ?

2) a..is supposed to be f(x) = 2x, 0 ≤ x < 1.

Last edited:
Just do a Cuil or Google search for mean, variance of a continuous random variable to
find out the formulas, and get back to us.

Let's just worry about the first problem to begin. You really need the definition of a pdf to do this problem. How do you express $\mathbf{P}\{X \in A\}$ for a set A in terms of the pdf?

Write out the definitions mentioned above and then try to use them to solve the problems. We can't help you further until you show some work.