PMF Joint and Marginal PMFs 3

Question 1

Let X and Y have joint PMF p(x, y) = 1/6 for (x, y) ∈ {(1,1),(1,2),(2,1),(2,2),(3,1),(3,2)}. What is p_Y(1)?

Accepted Answer

1/2

Answer

1/6

Answer

1/3

Answer

2/3

Question 2

Which statement correctly describes the support of a joint PMF?

Accepted Answer

The set of pairs (x, y) where p(x, y) > 0

Answer

The set of all real-valued pairs (x, y)

Answer

The set of pairs (x, y) where p(x, y) = 1

Answer

All pairs where x = y

Question 3

For independent X ~ Binomial(2, 0.5) and Y ~ Bernoulli(0.5), what is p(X=1, Y=1)?

Accepted Answer

0.25

Answer

0.125

Answer

0.5

Answer

0.375

Question 4

Which of the following joint PMF tables corresponds to X and Y being independent?

Accepted Answer

p(1,1)=0.06, p(1,2)=0.14, p(2,1)=0.24, p(2,2)=0.56

Answer

p(1,1)=0.3, p(1,2)=0.1, p(2,1)=0.2, p(2,2)=0.4

Answer

p(1,1)=0.25, p(1,2)=0.25, p(2,1)=0.25, p(2,2)=0.25

Answer

p(1,1)=0.4, p(1,2)=0.1, p(2,1)=0.1, p(2,2)=0.4

Question 5

If X and Y are discrete random variables, E[g(X, Y)] is computed as:

Accepted Answer

∑_x ∑_y g(x, y) · p(x, y)

Answer

∑_x ∑_y g(x, y) · p_X(x) · p_Y(y)

Answer

∑_x g(x) · ∑_y g(y)

Answer

g(E[X], E[Y])

Question 6

Given p(0,0)=0.1, p(0,1)=0.4, p(1,0)=0.2, p(1,1)=0.3, what is E[X·Y]?

Accepted Answer

0.3

Answer

0.1

Answer

0.5

Answer

0.7

Question 7

For a joint PMF p(x, y), the covariance Cov(X, Y) is computed as:

Accepted Answer

E[XY] − E[X]·E[Y]

Answer

E[X²Y²] − E[X]²E[Y]²

Answer

E[(X + Y)²] − (E[X] + E[Y])²

Answer

Var(X) + Var(Y)