Question

An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (An ordinary (fair) coin is tossed 3 times. Ou) and "tails" () which we write , , etc. For each outcome, let be the random variable counting the number of tails in each outcome. For example, if the outcome is , then . Suppose that the random variable is defined in terms of as follows: . The values of are thus:Outcome Value of Calculate the probability distribution function of , i.e. the function . First, fill in the first row with the values of . Then fill in thevalue x of X Px(X)

Answer 1

Probability distribution

X P(X)

0 1/8

1 3/8

2 3/8

3 1/8

Explanation:

When a coin is tossed there are two outcomes head and tail. When three coins are tossed the possible outcomes are

Sample space=S={HTH,THH,TTH,HHH,HTT,THT,TTT,HHT}

The total number of outcomes is n(S)=8. The X be the random variable counting number of tails in each outcome and so X can take values as 0,1,2,3. The probabilities can be computed as P(X)=n(X)/n(S). The probabilities are calculated as under:

X Outcomes P(X)

0 HHH 1/8

1 HHT,THH,HTH 3/8

2 TTH,HTT,THT 3/8

3 TTT 1/8

The probability distribution of X is as under:

X P(X)

0 1/8

1 3/8

2 3/8

3 1/8