Final answer:
The cumulative distribution function of a binomial random variable with n=3 and p=1/2 can be found by adding the probabilities of obtaining 0 to 3 successes in a binomial experiment.
Step-by-step explanation:
The student is asking to determine the cumulative distribution function (CDF) for a binomial random variable with parameters n = 3 and p = 1/2. A binomial distribution is characterized by outcomes being classified as 'success' or 'failure', with the same probability of success p on each trial out of n independent trials.
For this binomial distribution situation, we calculate the probabilities for each possible outcome X, where X can be 0, 1, 2, or 3 since there are three trials. To find the CDF, we cumulatively add up the probabilities of achieving 0, 1, 2, or 3 successes using the binomial probability formula.
The CDF values for each possible outcome can be calculated using the formula binomcdf(n, p, X), where X is the number of successes we want the probability for.
- P(X ≤ 0) would be the probability of obtaining 0 successes.
- P(X ≤ 1) would add the probabilities of obtaining 0 or 1 success.
- P(X ≤ 2) would add the probabilities of obtaining 0, 1, or 2 successes.
- P(X ≤ 3) sums all probabilities, which should be 1 as it includes all possible outcomes.