Suppose you were given two unfair coins with PH 23 and a fa

Suppose you were given two unfair coins with P(H) = 2/3 and a fair die with face of each die is marked with

numbers 0,1,2,3,4 and 5. If you toss two coins and roll the die at the same time,

a) What is the sample space (list all possible outcomes)?

b) Suppose the outcomes of the coin, “H” is marked as “1” and “0” for “T”. Let X be a random variable representing the sum of three outcomes, what are the possible values for X?

c) What is the probability of each outcome of X? (Hint: give the probability distribution)

Solution

We are given that

two unfair coins with P(H) = 2/3 and a fair die with face of each die is marked with

numbers 0,1,2,3,4 and 5.

And the experiment is tossing a two coins and roll the die at the same time.

a) What is the sample space (list all possible outcomes)?

sample space () = { HH0 HH1 HH2 HH3 HH4 HH5 HT0 HT1 HT2 HT3 HT4 HT5
TH0 TH1 TH2 TH3 TH4 TH5 TT0 TT1 TT2 TT3 TT4 TT5 }

n() = 24

b) Suppose the outcomes of the coin, “H” is marked as “1” and “0” for “T”. Let X be a random variable representing the sum of three outcomes, what are the possible values for X?

That is outcomes of the coin \"H\" is marked as \"1\" and \"T\" is marked as \"0\".

Let X be a random variable representing the sum of three outcomes.

The possible values of X are 0,1,2,3,4,5,6 and 7.

c) What is the probability of each outcome of X? (Hint: give the probability distribution)

P(X=0) = 1/24

P(X=1) = 3/24

P(X=2) = 4/24

P(X=3) = 4/24

P(X=4) = 4/24

P(X=5) = 4/24

P(X=6) = 3/24

P(X=7) = 1/24

The probability distribution of X is,

1