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How to Find E in Estimated Proportions

In statistics, the expected value (E) tends to come in the form of a continuous variable. This occurs because many of the distributions commonly appearing in statistical texts and studies are continuous, meaning that the expected values are also continuous numbers, often representing “average” values. Expected values, however, exist for most distributions, including the discrete distribution that deals with proportions, the binomial distribution. To find E in estimated proportions, you need to observe the parameters inside the binomial distribution of interest.

Instructions

- 1
  Rewrite the binomial distribution in its mathematical form. It should appear as a probability being equated to a function with a function of three variables, often called “n,” “k” and “p.”
- 2
  Match the binomial distribution of interest to its general form and compare the values. The general form is P(X = k) = nCk*p^k*(1-p)^(n-k).
- 3
  Locate the value that equates to “p.” This is the expected value in estimated proportions. For example, if your binomial distribution is P(X = k) = 10Ck*(1/3)^k*(2/3)^(10-k), it should be clear that p = 1/3 in this equation. Thus, E in estimated proportions is 1/3.

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