Statistics question Continous Random Variables

[XodoX]

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.

 

[spamiam]

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.

 

[XodoX]

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.

 

[Bacle]

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.

 

[spamiam]

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.