(i)[4]
Construct the probability distribution table for $Y$.
(ii)[1]
Find the expectation of $Y$.
Mathematics 9709 · AS & A Level · Linear combinations of random variables
Linear combinations of random variables — practice question
The random variable $X$ follows the probability distribution given in the table: $x = 2, 4, 6$ with $P(X = x) = 0.5, 0.4, 0.1$. Two independent values of $X$ are selected at random. The random variable $Y$ is $0$ when the two values of $X$ match. Otherwise, $Y$ equals the larger value of $X$ minus the smaller value of $X$.