7 The independent random variables \(X\) and \(Y\) have the distributions \(\operatorname { Po } ( 1.9 )\) and \(\operatorname { Po } ( 2.2 )\) respectively.
- Find \(\mathrm { P } ( X + Y < 4 )\).
\includegraphics[max width=\textwidth, alt={}, center]{7c078a14-98f9-4292-ae76-a2642238176f-10_74_1581_406_322}
\includegraphics[max width=\textwidth, alt={}, center]{7c078a14-98f9-4292-ae76-a2642238176f-10_75_1581_497_322} - Find the probability that \(X = 2\) given that \(X + Y < 4\).
\includegraphics[max width=\textwidth, alt={}, center]{7c078a14-98f9-4292-ae76-a2642238176f-10_2715_35_144_2012} - A sample of 60 randomly chosen pairs of values of \(X\) and \(Y\) is taken,and the value of \(X + Y\) is calculated for each pair.The sample mean of these 60 values is found.
Find the probability that the sample mean of \(X + Y\) is less than 4.0 .
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