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QUESTION 1 Consider a random variable with a binomial distribution, with 35 trials and probability of success equals to 0.5.

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Answer #1

1) n = 35

p = 0.5

Expected value = n * p = 35 * 0.5 = 17.5

2) n = 10

p = 0.54

P(X = 4) = 10C4 * 0.544 * (1 - 0.54)10-4 = 0.169

3) n = 10

p = 0.56

P(X = 4) = 10C4 * 0.564 *(1 - 0.56)10-4 = 0.150

4) n = 10

p = 0.33

P(X = 4) = 10C4 * 0.334 * (1 - 0.33)10-4 = 0.225

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