Thread: chi squared

Suppose that six random variables X1,...X6 for a random sample from a standard normal distribution and let Y= (X1+X2+X3)^2 + (X4+X5+X6)^2
Determine a value of c such that the random variable cY will have a chisquared distribution

Any clues on this?? Thanks!

Originally Posted by holly123

Suppose that six random variables X1,...X6 for a random sample from a standard normal distribution and let Y= (X1+X2+X3)^2 + (X4+X5+X6)^2
Determine a value of c such that the random variable cY will have a chisquared distribution

Any clues on this?? Thanks!

The first thing I'd do is get the (well known) distributions of U1 = X1 + X2 + X3 and U2 = X4 + X5 + X6.

Then I'd think about the distributions of V1 = U1^2 and V2 = U2^2, and I'd also be thinking about the well known distribution of X^2 .....

Then I'd be thinking about the distribution of W = V1 + V2, in light of the above.

Originally Posted by holly123

Suppose that six random variables X1,...X6 for a random sample from a standard normal distribution and let Y= (X1+X2+X3)^2 + (X4+X5+X6)^2
Determine a value of c such that the random variable cY will have a chisquared distribution

Any clues on this?? Thanks!

The sum of the squares of k standard normal RV's has a chi-squared distribution with k degrees of freedom.

CB