Question

Exercise 2. Consider n independent trials, each of which is a success with probability p. The random variable X, equal to the total number of successes that occur, is called a binomial random variable with parameters n and p. We can determine its expectation by using the representation j=1 where X, is a random variable defined to equal 1 if trial j is a success and to equal otherwise. Determine ELX

Answer 1

Binomial Random Variable:

A type of discrete random variable used to count the number of occurences of an event in random sample in a binomial experiment.A binomial random variable can only be used to count whether a certain event occurs or does not occur and can not be used to measure partial states.

It can be as low as 0, if all the trails end up faiture(or) as hgh as n, if all n trails end in success.The random variable x that represents the number of success in those n trails is called binomial random variable and is determined by the value of n&p.

  $\sigma$²x = np(1-p)

  $\sigma$x = $\sqrt{}$ np(1-p)