<s>[INST] Let \(X\) be a normal random variable with mean \(\mu=6\) and variance \(\sigma^{2}=25\) Suppose that independently of \(X\) we have a random variable \(Y=Y_{1}+Y_{2}\), where \(Y_{1}\) and \(Y_{2}\) are independent Poisson random variables with means \(\lambda_{1}=2\) and \(\lambda_{2}=3\) respectively Then \(Y\) is a Poisson random variable with mean \(\lambda=5\), and since it is independent of \(X\), \(X\perp\!\!\!\perp Y\)[/INST]