Cumulative Distribution Function

[statjunior]

Please help me, I have 2 cases:

1. n is positive constant and defined by function f(x)=1/2.n.e^(-n.x) if x>=0 and f(x)=1/2.n.e^(-n.x) if x<0. Please explain if f(x) is cumulative distribution function (cdf)!

2. Please count E(X) and Var(X) from probability function f(x)=a.x^(a-1), 0<x<1, a>0!

I'm new in statistic, please lead me. Thanks.

[vinux]

Hint: Cumulative distribution function


You just need to integrate f(x)

[statjunior]

@vinux,
for the function:

is integrated into:


okay, but how can I sure that the f(x) is cdf?
and what about case number 2?

Thanks

[vinux]

Do it in two ranges..

first when x<0

and other when x>0

when x>0

where f1 and f2 according to the range

===================
sorry .I dint see your question properly..

f(x) is not a cdf..
for testing a function , say g(x) is cdf?

for and
and is an increasing function.

[statjunior]

Sorry for making you confused, here it is the questions:

1. Prove that f(x) is cumulative distribution function (cdf), where
   for and x<0, and is positive.
2. Find E(X) and Var(X) from function:
   
   where 0<x<1 and a>0!

Your clearly explanation and answer would be greatly appreciated. Thanks.

[vinux]

May be hint may not work for you.
1) It is not a cdf . because

I guess you are confused with density function and cumulative distribution function. For more understanding check this: http://en.wikipedia.org/wiki/Cumulat...ution_function.

2)


Now solve this you can calculate Var(X)

[statjunior]

uhmm sorry i'm very very new in statistic , but i'll try to understand it.
Thank you so much for your explanation, it helps me already.
I'll calculate it then post the final calculation here soon later.
Many thanks

[statjunior]

Here it is my calculation for question number 2:






But I'm still confused about question number 1, confused between cdf and pdf. I thought the f(x) is pdf, but don't know what calculation I should write to prove it.
I hope that I can understand this case, and would you mind to explain how a function can be cdf & how a function can be pdf by giving me some examples? Thank you so much.

[vinux]

Q2: is right.
Q1. pdf is the probability density function. Usually we write in small letter ( say f(x))
property of f(x) is

The cdf is the cumulative version of pdf. denoted by Capital letter ( say F(x) )



for example refer http://en.wikipedia.org/wiki/Probabi...nsity_function


Thumb rule is look at the shape of the curve.. if it is increasing non negative function with 1 is the suprimum.. then it is a cdf

or look at that graph ... if it is non negative function with area is one... then it is a pdf.