EXAMPLE 2.2.3. An experiment was carried out as follows. Five independent Bernoulli samples were drawn, with 7 = 0.3, fr

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Example 2 2 3 An Experiment Was Carried Out As Follows Five Independent Bernoulli Samples Were Drawn With 7 0 3 Fr 1 (39.82 KiB) Viewed 105 times

Please show me the steps to verify this example.
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EXAMPLE 2.2.3. An experiment was carried out as follows. Five independent Bernoulli samples were drawn, with 7 = 0.3, from a population of N = 10 elements. Once drawn, each sample was replaced into the population. The results are shown in the following table, where a “l” denotes that the element was selected, and a “O” denotes that the element was not selected.
Sample 3 Element 1 2 4 5 5 1 2 3 4 5 6 7 8 9 10 1 0 0 0 0 0 0 0 0 0 1 0 1 0 1 0 0 1 1 0 0 0 1 0 1 0 1 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 1 0 0 0 0 NiOOOO 1 5 4 4 Number of selected elements In this experiment, the realized sample sizes vary from 1 to 5. Each sample size is a realization of a Bin(10,0.3) random variable, that is, a binomially distributed random variable with parameters 10 and 0.3, so the expected size of each sample is 10.0.3 = 3. The number of times that a given element is pičked varies in this example between 0 and 4. This number is a realization of a Bin(5,0.3) random variable. The expected number of times each element is selected over the five repeated samples is thus 5.0.3 = 1.5.