Question

1. Toss a coin twice and create a probability distribution table. Write the possible values of the Random Variable x in one column and the probabilities in another column. Let X be the number of tails in two tosses of a coin. a) What are the possible values of the random variable x? Write these numbers on the left column and the probabilities on the right column. This problem is similar to the example in my video. b) Is this a probability distribution? Explain. X P(x) c) Find the mean and standard deviation of the probability distribution. Calculate the mean by hand but you may use the calculator to calculate the standard deviation. (note: the notation for the standard deviation of a probability distribution is the population standard deviation, denoted as o)

Answer 1

a) The possible values of the random variable X, representing the number of tails in two coin tosses, are 0, 1, and 2. We can write these numbers in the left column and assign probabilities to each outcome in the right column.

X P(x)
0 1/4
1 1/2
2 1/4

b) Yes, this is a probability distribution because the sum of all probabilities is equal to 1 and all probabilities are non-negative.

c) To calculate the mean, we multiply each value of X by its corresponding probability and sum them up. The mean is (0 * 1/4) + (1 * 1/2) + (2 * 1/4) = 1.

To calculate the standard deviation, you can use a calculator or statistical software.