Expected Value & Binomial Probabilities

Front

What is the definition of expected value in probability?

Back

The expected value is the average of all possible outcomes of a random variable, weighted by their probabilities.

Front

What are binomial probabilities?

Back

Binomial probabilities refer to the probabilities of obtaining a fixed number of successes in a fixed number of independent Bernoulli trials.

Front

What are the four key conditions for a binomial experiment?

Back

1. Fixed number of trials. 2. Each trial results in success or failure. 3. Trials are independent. 4. The probability of success is constant.

Front

What does 'n' represent in the binomial probability formula?

Back

The number of trials.

Front

What does 'p' represent in the binomial probability formula?

Back

The probability of success on a single trial.

Front

What does 'r' represent in the binomial probability formula?

Back

The number of successes in the n trials.

Front

What is the formula for calculating the expected value in a binomial distribution?

Back

Expected Value (E) = n * p, where n is the number of trials and p is the probability of success.

Front

How do you calculate the probability of getting exactly r successes in n trials?

Back

Use the binomial probability formula: P(X = r) = (nCr) * (p^r) * (q^(n-r)), where q = 1 - p.

Front

What is the mean of a binomial distribution?

Back

The mean is equal to the expected value, which is n * p.

Front

What is the variance of a binomial distribution?

Back

Variance = n * p * q, where q = 1 - p.