Exercise 2. Consider n independent trials, each of which is a success with probability p. The...

 

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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 n X = [X j=1 where X, is a random variable defined to equal 1 if trial j is a success and to equal 0 otherwise. Determine E[X]. 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 n X = [X j=1 where X, is a random variable defined to equal 1 if trial j is a success and to equal 0 otherwise. Determine E[X].

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