Question

The next three questions (5 to 8) refer to the following:

An unfair coin is tossed three times. For each toss, the probability that the coin comes up heads is 0.6 and the probability that the coin comes up tails is 0.4.

If we let X be the number of coin tosses that come up heads, observe that the possible values of X are 0, 1, 2, and 3. Find the probability distribution of X.

Hint: the problem can be solved in two different ways as described below. Both methods will result in the same answer.

Method 1: Write out the sample space of possible outcomes, obtain the probability of each of the outcomes, and relate each of these outcomes to X = 0, X = 1, X = 2, or X = 3.

Method 2: Verify that the four requirements of the binomial setting are satisfied in this problem. Use the binomial formula for each possible value of X to obtain the probability distribution of X.

(If you only know how to solve the problem with one method, please be sure to check the assignment solutions after the due date to understand the other method.)

Question 5 (0.5 points)

Saved

What is P(X = 0)?

Your Answer:

Question 5 options:

Answer

Question 6 (0.5 points)

Saved

What is P(X = 1)?

Your Answer:

Question 6 options:

Answer

Question 7 (0.5 points)

Saved

What is P(X = 2)?

Your Answer:

Question 7 options:

Answer

Question 8 (0.5 points)

Saved

What is P(X = 3)?

Your Answer:

Question 8 options:

Answer

Answer 1

X does satisfy the the requirements to be considered a binomial distribution. There are 3 independent trials, and the probability of success(getting a heads) in each trial is 0.6. In terms of notation, we can write,X~Bin(3,0.6)

Therefore, the distribution of X is:

. This follows from the definition of the

probability distribution of a binomial Random Variable.

QUESTION 5:

QUESTION 6:

QUESTION 7:

QUESTION 8: