BSAN Binomial Distribution

A random experiment with exactly two possible outcomes: success or failure

What is a Bernoulli trial?

The number of successes in a fixed number of independent Bernoulli trials

What does a binomial random variable measure?

Fixed number of trials, two possible outcomes, independent trials, and constant probability of success.

What four conditions are required for a binomial distribution?

The outcome being counted, regardless of whether it is good or bad

What does "success" mean in a binomial experiment?

n = number of trials; p = probability of success in each trial

What are the two parameters of a binomial distribution?

Because the outcome of one trial must not affect the outcomes of the other trials

Why must binomial trials be independent?

Because it counts successes and can only take whole-number values.

Why is a binomial random variable discrete?

When finding the probability of exactly a specific number of successes

When should you use the binomial PMF?

When finding the probability of a certain number of successes or fewer

When should you use the binomial CDF?

The probabilities are balanced around the center

What does a symmetric binomial distribution look like?

A distribution with a longer tail on one side

What is a skewed binomial distribution?

A distribution with one main peak

What does unimodal mean?

Yes. The binomial formula works even when the distribution is skewed

Can you still use the binomial formula if the symmetry conditions aren't satisfied?

P( a ≤ X ≤ b), including both endpoints

What does "between a and b, inclusive" mean?

The average number of successes across many repetitions of the experiment

What does the expected value of a binomial distribution represent?

Variance measures spread in squared units, while standard deviation measures spread in the original units.

What's the difference between variance and standard deviation?