Question-54
Chi-square Distribution
Let \(X_1 \sim {\chi}^2_{8}\) and \(X_2 \sim {\chi}^2_{7}\) are indepdendent random variables. Define a new random variable \(Y = X_1 + X_2\). What is the Var\((Y)?\)
Hint
Use the concept of ``Additive property of Chi-square distribution”, i.e., if \(X_1 \sim {\chi}^2_{n_1}\) and \(X_2 \sim {\chi}^2_{n_2}\) are indepdendent random variables, then \(X_1 + X_2 \sim {\chi}^2_{n_1 + n_2}\) and use the formula of variance of a chi-square random variable.
Answer
Solution