let x1 Xn be a random sample from a normal distribution wit

let x1 ...... Xn be a random sample from a normal distribution with parameters mu and sigma^2. what is teh probability distribution of the random variable (n-1)s^2 / sigma^2 and its associated degrees of freedom?

A) t- distribution with n degrees of freedom

B) chi square with n-1 degrees of freedom

C) chi square with n-2 degrees of freedom

D) t- distribution with n-1 degrees of freedom

Solution

random variable = (n-1)s^2 / sigma^2

AS THE DEGREE OD FREEDOM = N-1

THEREFORE FOR THIS RANDOM VARIABLE DEGREE OF FREEDOM = N-1-1 = N-2

AND WE ONLY HAVE ONE OPTION WITH N-2 DEGREEOF FREEDOM HENCE THE CORRECT OPTION HERE WILL BE C= CHI SQUARE WITH N-2 DEGREE OF FREEDOM.