- #1

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## Homework Statement

Let X and Y be two random variables, with joint distribution given by the following table:

Code:

```
a
b 1 2 3 4
--------------------------------------
1 16/136 3/136 2/136 13/136
2 5/136 10/136 11/136 8/136
3 9/136 6/136 7/136 12/136
4 4/136 15/136 14/136 1/136
```

What is:

a.) P(X = Y)

b.) P(X + Y = 5)

c.) P(1 < X <= 3, 1 < Y <= 3)

d.) p((X,Y) [tex]\in[/tex] {1,4} x {1,4})

## Homework Equations

## The Attempt at a Solution

To be honest, I'm not exactly sure what exactly these kinds of operators mean (e.g. what does it mean to say P(X = Y). But here's what I have so far:

P(a = 1) = P(a = 2) = P(a = 3) = P(a = 4) = P(b = 1) = P(b = 2) = P(b = 3) = P(b = 4) = 34/136

a.) P(X = Y) is [P(a = 1, b = 1) + ... + P(a = 4, b =4)] = 16/136 + 10/136 + 7/136 + 1/136

b.) P(X + Y = 5) = [P(a = 1, b = 4) + P(a = 4, b = 1)] = 13/136 + 4/136

c.) P(1 < X <= 3, 1 < Y <= 3) = c.) P(1 < a <= 3, 1 < b <= 3) =

10/136 + 11/136 + 6/136 + 7/136

d.) p((X,Y) [tex]\in[/tex] {1,4} x {1,4}) = ? I have no idea what this syntax means