Question

Consider 2 triangular dies (each has 4 faces) one blue and another red.

Let Y be a random variable associated with the result of the blue dice. Let X be a random variable that takes the maximum of the two showing numbers.

1. What is the joint distribution of X and Y (draw a table)

2. Calculate the marginal distributions of X and Y.

3.Are X and Y independent? Justify.

Answer 1

1) Joint distribution of X and Y:

2) Marginal distribution of X (g(x)) and marginal distribution of Y (h(y)):

3) X and Y are dependent:

P(X=1 and Y=4)$\neq$ P(X=1)*P(Y=4)

0$\neq$1/16*1/4