You could have squared everything and obtain an
It looks like
I have a homework problem asking me to find the constant c that will make the statistic have a t-distribution. The rv X1...X5 are iid with a standard normal distribution.
The statistic is:
T = c(X1 + X2)/sqrt (X3^2+X4^2+X5^2)
I see that the denominator looks like a Chi-Square with 3df and the numerator could be the summation of X. I know I need X-N(0,1) in numerator and U-Chi(rdf) in denominator for a t-distribution t(rdf). I want to square both sides to start but that looks more like a F-distribution. Any hints would be appreciated.
I am trying to understand the math operations that apply. Do you treat the tilde (~) like an equal sign and then you can perform math operations across it. It looks like you subtrated mu from both sides and then divided by sigma squared but you ended up with sigma instead of sigma squared under the X-mu. Can you clearify the math operations for me.