Bernoulli Trials and Binomial Distribution

The video tutorial covers Bernoulli trials and the binomial distribution. It explains Bernoulli trials as simple probability experiments with two outcomes, success and failure, and how they can be represented as discrete random variables. The tutorial provides examples using coin flips, card draws, and voter approval. It introduces the binomial distribution as a sum of Bernoulli trials and explains how to calculate probabilities, mean, and variance. The video also demonstrates constructing probability histograms for binomial distributions.

What is a Bernoulli trial?

• A trial with three outcomes

• A trial with no outcomes

• A trial with exactly two outcomes

• A trial with more than two outcomes

In a Bernoulli trial, what are the two possible outcomes traditionally called?

• Pass and Fail

• True and False

• Success and Failure

• Win and Lose

What is the probability of success when flipping a fair coin?

• 1/3

• 1

• 1/2

• 1/4

How is success encoded in a Bernoulli trial when viewed as a discrete random variable?

• As 0

• As 1

• As 2

• As -1

What is the expected value of a Bernoulli trial?

• 1

• 1 - p

• p

• 0

What is the variance of a Bernoulli trial?

• p * (1 - p)

• 1 - p

• p + (1 - p)

• p

What is the standard deviation of a Bernoulli trial?

• Square root of (1 - p)

• Square root of p

• Square root of (p * (1 - p))

• p * (1 - p)

What is the binomial distribution?

• A distribution for random variables with no outcomes

• A distribution for random variables with more than two outcomes

• A distribution for discrete random variables

• A distribution for continuous random variables

In a binomial distribution, what does 'n' represent?

• Probability of failure

• Probability of success

• Number of trials

• Number of successes

In a binomial distribution, what does 'p' represent?

• Number of trials

• Probability of failure

• Number of successes

• Probability of success