MHB Derivation of snedecors F distribution

[coolamko12]

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?

 

[Siron]

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 $\frac{X_1/n_1}{X_2/n_2} \sim F(n_1,n_2)$.