Binomial Distribution Binomial Experiment- A?binomial experiment?(also known as a?Bernoulli trial) is a?statistical experiment?that has the following properties: The experiment consists of?n?repeated trials. Each trial can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. The probability of success, denoted by?P, is the same on every trial. The trials are?independent; that is, the outcome on one trial does not affect the outcome on other trials. Consider the following statistical experiment. You flip a coin 2 times and count the number of times the coin lands on heads. This is a binomial experiment because: The experiment consists of repeated trials. We flip a coin 2 times. Each trial can result in just two possible outcomes - heads or tails. The probability of success is constant - 0.5 on every trial. The trials are independent; that is, getting heads on one trial does not affect whether we get heads on other trials. Notation The following notation is helpful, when we talk about binomial probability. k: The number of successes that result from the binomial experiment. n: The number of trials in the binomial experiment. P: The probability of success on an individual trial. Q: The probability of failure on an individual trial. (This is equal to 1 -?P) Binomial Distribution A?binomial random variable?is the number of successes?x?in?n?repeated trials of a binomial experiment. The?probability distribution?of a binomial ran ...
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