Question

Consider tossing a fair coin twice. Denote X as the total number of tail(s) in two tosses and Y as the number of head at the second toss. Find the joint probability mass function (PMF) Pₓᵧ(x,y).

Answer 1

The joint probability mass function (PMF) Pₓᵧ(x,y) for the random variables X and Y can be determined by considering the possible outcomes of tossing a fair coin twice.

Step-by-step explanation:

The joint probability mass function (PMF) Pₓᵧ(x,y) for the random variables X and Y can be determined by considering the possible outcomes of tossing a fair coin twice.

Since each toss of a fair coin has two equally likely outcomes (head or tail), the sample space for two tosses is {HH, HT, TH, TT}, where H represents a head and T represents a tail.

The joint PMF is given by:

Pₓᵧ(x,y) = P(X=x, Y=y) = P(two tails) = P(TT) = 1/4

Since the joint PMF for X and Y is simply the probability of obtaining two tails, which is 1/4, for any value of x and y.