Question

What is the expected value of the binomial distribution where n = 16 and p = 0.85?

Answer 1

Given:

n = 16

p = 0.85

To find:

expected value =?

Step-by-step explanation:

• In a probability distribution, the average value of possible values of a random variable, with weights given by their respective theoretical probabilities, is known as the expected value.
• Usually, it is represented by E{x}.
• The expected value of a binomial distribution with n trials is the average number of successes.
• Let X be a discrete random variable with the binomial distribution with parameters n and p for some n∈N and 0≤p≤1.
• Then the expectation of X is given by:

        E{X} = np

• Put the given values in above equation:

        E{X} = (16) (0.85)

        E{X} = 13.6

• Hence the expected value of the binomial distribution is 13.6 .