Chapter 2: Problem 14
Let \(X_{1}, X_{2}\) be two random variables with joint \(\mathrm{pmf} p\left(x_{1}, x_{2}\right)=(1 / 2)^{x_{1}+x_{2}}\), for \(1 \leq x_{i}<\infty, i=1,2\), where \(x_{1}\) and \(x_{2}\) are integers, zero elsewhere. Determine the joint mgf of \(X_{1}, X_{2}\). Show that \(M\left(t_{1}, t_{2}\right)=M\left(t_{1}, 0\right) M\left(0, t_{2}\right)\).
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.