## BINOMIAL AND NORMAL RANDOM VARIABLES

Let X be the number of successes in n independent trials of some experiment whose outcome is “success” or “failure” when the probability of success in each trial is p. Such a random variable often appears in practice (for example, the number of heads in n tosses) and is called a binomial random variable. More formally we state

DEFINITION 5.1.1 Let (FJ, г = 1, 2, be mutually independent

with the probability distribution given by

**(5.1.1) **F,- = 1 with probability/?

= 0 with probability 1 — p = q.

Then the random variable X defined by

П

**(5.1.2) **X = X Y{

i=1

is called a binomial random variable. Symbolically we write X ~ Bin, p).

Note that Fj defined in (5.1.1) is distributed as 5(1, p), which is called a binary or Bernoulli random variable.

theorem 5...

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