Question

A coin is biased so that head appears with probability 2/3 and tails with probability 1/3 This coin is tossed three times. If X denotes the number of heads occuring and Y denotes the number of tails that occur up to the first head, if any that appears, then determine the joint pmf of X and Y

Answer 1

Answer:

Given a biased coin such that heads is 3 times as likely as tails. The coin is tossed twice.

P(H) = 3434 and P(T) = 1414

Let X be the random variable for the number of tails.

P (X = 0) = P (HH) =3/4*3/4=9/1634×34=916

P (X = 1) = P (HT, TH) =3/4*1/4+3/4*1/4=3/834×14+34×14=38

P (X = 2) = P (TT) = 1/4*1/4=1/16

14×14=116

Therefore the probability distribution is as follows:  

X  : P(X)

0      9/16

1        3/8

2      1/16

Step-by-step explanation: