MHB Derivation of snedecors F distribution

Click For Summary
The F distribution is derived from the ratio of two independent chi-squared variables, specifically when X1 follows a chi-squared distribution with n1 degrees of freedom and X2 with n2 degrees of freedom. The relationship is expressed as (X1/n1) / (X2/n2) following an F distribution with parameters n1 and n2. The moment-generating function (mgf) can be utilized to find the raw moments of the F distribution. Additionally, the mean and variance can be calculated, with the mean being n2 / (n2 - 2) for n2 > 2, and the variance being [2n2^2(n1 + n2 - 2)] / [n1(n2 - 2)^2(n2 - 4)] for n2 > 4. This derivation and properties are crucial for statistical analysis involving the F distribution.
coolamko12
Messages
1
Reaction score
0
derive f distribution as x1 and x2 are independent random variables having a chi-square distribution with n1 and n2 degrees of freedom.. aslo mgf and find raw moments ... and finds its mean and variance.?prove it ?help me guys?
 
Physics news on Phys.org
coolamko12 said:
derive f distribution as x1 and x2 are independent random variables having a chi-square distribution with n1 and n2 degrees of freedom.. aslo mgf and find raw moments ... and finds its mean and variance.?prove it ?help me guys?

There's a theorem which states that the $F$ distribution can be defined as the fraction of two independent chi-squared distributions. More precisely,

If $X_1 \sim \chi_{n_1}^2$ and $X_2 \sim \chi_{n_2}^2$ are two independent chi-squared distributions then $\frac{X_1/n_1}{X_2/n_2} \sim F(n_1,n_2)$.
 

Thread 'Two interesting number theory tricks'

First trick I learned this one a long time ago and have used it to entertain and amuse young kids. Ask your friend to write down a three-digit number without showing it to you. Then ask him or her to rearrange the digits to form a new three-digit number. After that, write whichever is the larger number above the other number, and then subtract the smaller from the larger, making sure that you don't see any of the numbers. Then ask the young "victim" to tell you any two of the digits of the...
View full post »

Similar threads

MHB Distribution and Density functions of maximum of random variables
  • · Replies 6 ·
Replies
6
Views
4K
Graduate Proving Lim F(x,y) is the Distribution Function for X
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Why does normal distribution turn into t distribution when variance is unknown?
  • · Replies 5 ·
Replies
5
Views
5K
Graduate Estimation error from estimation quantile of normal distribution
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Bivariate normal distribution from normal linear combination
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad Probability-To-Exceed (PTE) and Chi^2 distribution
  • · Replies 5 ·
Replies
5
Views
4K
Graduate Combining model uncertainties with analytical uncertainties
  • · Replies 2 ·
Replies
2
Views
1K
Sample distribution and expected value.
  • · Replies 5 ·
Replies
5
Views
2K
Transforming Two Normal Random Variables into a Non-Central F Distribution
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Fourier Transform of a Probability Distribution
  • · Replies 9 ·
Replies
9
Views
5K