Question

Look at the relative-frequency table below of the probability distribution of the discrete random variable X, with X = "the number of pets in a household."

x P(X = x)
0 .09
1 .29
2 .42
3 .15
4 .05
What is the expected value of pets in a randomly selected household?

Answer 1

Answer: The expected value of a discrete random variable is calculated by multiplying each possible value of the variable by its corresponding probability, and then adding up all of the products. Symbolically, the expected value of X is:

E(X) = Σ [x * P(X = x)]

where the summation is taken over all possible values of X.

Using the table given, we can calculate the expected value of pets in a randomly selected household as follows:

E(X) = 0*(.09) + 1*(.29) + 2*(.42) + 3*(.15) + 4*(.05)

E(X) = 0 + 0.29 + 0.84 + 0.45 + 0.20

E(X) = 1.78

Therefore, the expected value of pets in a randomly selected household is 1.78.

Explanation: