Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The distributions of the independent random variables $X$ and $Y$ are, respectively, $\text{Po}(1.9)$ and $\text{Po}(2.2)$.
(a)[3]
Determine $P(X + Y < 4)$.
(b)[4]
Find the probability that $X = 2$ on condition that $X + Y < 4$.
(c)[6]
A sample of $60$ randomly selected pairs of $X$ and $Y$ values is collected, and $X + Y$ is worked out for every pair. The mean of these $60$ values is then calculated. Find the probability that the sample mean of $X + Y$ is below $4.0$.
Worked solution & mark scheme
This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Work out $\lambda=1.9+2.2=4.1$” …