[tex]1=\frac{256}{625}[/tex]
Binomial Distribution:
- The binomial distribution with parameters [tex]n[/tex] and [tex]p[/tex] is the discrete probability distribution of the number of successes in a series of [tex]n[/tex] independent experiments, each asking a yes-or-no question and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability [tex]q=1p[/tex]).
- This distribution is used in probability theory and statistics.
- A Bernoulli trial, or experiment, is another name for a single success-or-failure experiment, and a Bernoulli process is another name for a series of results.
- For a single trial, or [tex]n=1[/tex], the binomial distribution is a Bernoulli distribution.
- The popular binomial test of statistical significance is based on the binomial distribution.
Therefore, the expected value for the binomial distribution below is [tex]1=\frac{256}{625}[/tex].
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