Question

Define (x,y,θ) ~ P(x,y,θ) as follows:

θ ~ Unif{0.1,0.9}

(x,y) |θ ~ Bern(x|θ) Bern(y|θ)

Where Bern(. | θ) is the p.m.f. for a Bernoulli random variable which takes the value 1 or 0 with probability, θ, (1-θ) respectively. Find probabilities

a) Pr(x=0, y=0) ? (enter answer in decimal form, e.g. 0.56 )

(b) Pr(x=1, y=1) ? (enter answer in decimal form, e.g. 0.56 )

(c) Pr(x=1, y=0)   ? (enter answer in decimal form, e.g. 0.56 )

(d) Pr(x=0, y=1) ? (enter answer in decimal form, e.g. 0.56 )

(e) What is the marginal distribution of x ?

(f) Is the marginal distribution of x the same as the marginal distribution of y?

Answer 1