Page 40 - FINAL CFA I SLIDES JUNE 2019 DAY 3
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LOS 10.e: Define a Discrete Uniform Random Session Unit 3:
Variable, a Bernoulli random variable, and a binomial
random variable. 10. Common Probability Distributions (A)
LOS 10.f: Calculate and interpret p given the discrete uniform and the binomial df, p.218
Experiment in which each trial is independent and only 2 (bi) outcomes: “success” or “failure.” Called Bernoulli random variable
if only 1 trial!
Lets say you pick from a large Bowl of White (W) and Black (B) Beans (only 2 outcomes) and each pick is replaced before
another pick (independence), and 60% is Black Beans.
What is the p of selecting exactly 3B in 5 (consecutive) days trials?
One way is BBBWW! If p(B) = 60%, then p(W) = 1- p(B) = 40% (Only 2 outcomes)
0.6*.6*.6 * .4*.4 = 3.56% But, How about: BWBBW, BBWBW, WBBBW, WWBBB, etc.
Hence
Recall nCr? 5C3 = n!/r(n-r!) = 5!/3!(5-3!) = 10
p (3B in 5 days) = 10 * 3.56% = 34.56%
