For example, suppose we flip a coin 5 times and we want to know the probability of obtaining heads k times. We would say that the random variable X follows a Binomial distribution.
For example, suppose we flip a coin 3 times. We can use the formula above to determine the probability of obtaining 0 heads during these 3 flips:. Here are a couple important notes in regards to the Bernoulli and Binomial distribution:. A random variables that follows a Bernoulli distribution can only take on two possible values, but a random variable that follows a Binomial distribution can take on several values. For example, in a single coin flip we will either have 0 or 1 heads.
However, in a series of 5 coin flips we could have 0, 1, 2, 3, 4, or 5 heads. A binomial distribution is the sum of independent and identically distributed Bernoulli random variables. If the coin lands heads, you win one dollar.
If the coin lands tails, you win nothing. The random variable that represents your winnings after one coin toss is a Bernoulli random variable. What is the probability that you win exactly three dollars in five tosses? That would require you to toss the coin five times, getting exactly three heads and two tails. A Bernoulli distribution is a special case of binomial distribution. Another way to say this is that a binomial random variable is the sum of independent and identically distributed Bernoulli random variables.
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