Final answer:
The expected value of a binomial random variable X with n = 8 and p = 0.9 is calculated using the formula µ = np. It equates to 7.2, indicating the average number of successes in this binomial distribution.
Step-by-step explanation:
The expected value of a binomial random variable X is given by the formula µ = np, where n is the number of trials and p is the probability of success on any given trial. For the binomial random variable with n = 8 and p = 0.9, the expected value can be calculated as follows:
- First, determine the number of trials (n), which is 8 in this case.
- Next, determine the probability of success (p), which is 0.9.
- Then, use the formula to calculate the expected value: µ = np = 8 * 0.9.
- Therefore, the expected value of X is 7.2.
The expected value of X tells us the average number of successes we would expect if we were to perform the same binomial experiment a large number of times under identical conditions.