# Unifrom distribution ?

1. May 20, 2009

### rclakmal

Unifrom distribution ?????

a continuous random variable X is uniformly distributed in the interval 2<=X<=6 and can take no other value
1.what is the probability density function ?
2.find mean and standard deviation of X ?
3.obtain distribution function of X?

yr obviously i can answer for first two question .....

1.for a uniform function
PDF is f(x)=1/(b-a)====>f(x)=1/4

2.mean=a+b/2=2+6/2=4;
SD= (b-a)^2/12=4^2/12=16/12=4/3

but i have no idea how to do the third part ...please can anybody help me out.....what is distribution function of X ....Not only the answer .....theory behind it ......then i may be able to get the answer for my self

2. May 20, 2009

### Pyrrhus

Re: Unifrom distribution ?????

Look up the uniform distribution function

3. May 20, 2009

### rclakmal

Re: Unifrom distribution ?????

i dont understand u mate .....can u explain it a bit !!!!!!it will be really helpful thanks!!!!!!!!

4. May 20, 2009

### rclakmal

Re: Unifrom distribution ?????

hey no help for 3 hours .....i have provided all ma works and waiting for someone to help!!please tell me what is the distribution function ......how it is ddifer from PDF ????any idea ?//and how to approach it ????

5. May 20, 2009

### HallsofIvy

Staff Emeritus
Re: Unifrom distribution ?????

Which of the words in "Look up uniform distribution function" did you not understand?
You seem to not know what a "distribution function" is. Surely that definition is given in your text book or, if not, on the internet.

If you had done that you would have found that the "probability density function" is the derivative of distribution function and that the distribution function, the probability that the result is between a and b, is the integral, from a to b, of the density function.

6. May 20, 2009

### rclakmal

Re: Unifrom distribution ?????

yr thanks !!!!i did think like that ......but i was getting 1 as the answer .......is it correct???if it is correct then all the uniform distributions have the same distribution function that is 1.....if that so thanks for helping me .......

7. May 20, 2009

### HallsofIvy

Staff Emeritus
Re: Unifrom distribution ?????

You misinterpreted what I said. In fact, now that I look at it, I didn't say it very well! The "distribution function", F(x), gives the probability a value of between a and b by F(b)- F(a). F(x) itself is the anti-derivative of f(x) the constant of integration determined by F(2)= 0. In other words, it is $F(x)= \int_2^x f(x) dx$.

8. May 21, 2009

### rclakmal

Re: Unifrom distribution ?????

Ok then answer should be F(x)=x/4-1/2; am i correct now ........ii think so .......so i have another question ......is it the same function which is caled as cumulative density function (CDF)??

9. May 22, 2009

### chiro

Re: Unifrom distribution ?????

The F(X) is called the CDF or cumulative distribution function. What this means is that the CDF measures P(X <= A) instead of the usual PDF measure which is P(X = A) or as in the continuous case P(A < X < B).

So the CDF measures probability up till a certain point of X. So its like saying that if we wanted to find P(X < A) we sum all probabilities up to but less than A instead of say at just A.