- Let \(X\) and \(Y\) be random variables which take on the
values 0 and 1 with the following joint distribution:
|
\(Y = 0\) |
\(Y = 1\) |
| \(X = 0\) |
.1 |
0.3 |
| \(X = 1\) |
.2 |
0.4 |
- Compute the marginal distributions of \(X\) and \(Y\).
- Compute the conditional distribution of \(X\) given \(Y =
1\).
- Are \(X\) and \(Y\) independent?
- The number of calls in a call center in a given hour follows a
Poisson distribution with parameter \(3\). If there are no calls, then the bored
workers flip a fair coin until they get heads. Let \(X\) be the number of calls and \(Y\) the number of coin flips they make in a
given hour.
- Find the joint mass function of \(X\) and \(Y\).
- Are \(X\) and \(Y\) independent?
- (optional if you don’t know double integrals) Let \(U_1, U_2 \sim
\text{Unif}(-1, 1)\). Compute \[E[|U_1
- U_2|].\]