7 The independent random variables \(X\) and \(Y\) have the distributions \(\operatorname { Po } ( 2.1 )\) and \(\operatorname { Po } ( 3.5 )\) respectively.
- Find \(\mathrm { P } ( X + Y = 3 )\).
- Given that \(X + Y = 3\), find \(\mathrm { P } ( X = 2 )\).
- A random sample of 100 values of \(X\) is taken. Find the probability that the sample mean is more than 2.2.
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