?The chi-squared random variable with k degrees of freedom has moment-generating
Chapter 5, Problem 5.8.4(choose chapter or problem)
The chi-squared random variable with k degrees of freedom has moment-generating function \(M_{X}(t)=(1-2 t)^{-k / 2}\). Suppose that \(X_{1}\) and \(X_{2}\) are independent chi-squared random variables with \(k_{1}\) and \(k_{2}\) degrees of freedom, respectively. What is the distribution of \(Y=X_{1}+X_{2}\) ?
Text Transcription:
M_X(t)=(1-2t)^-k/2
X_1
X_2
k_1
k_2
Y=X_1+X_2
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