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Part 1: Discrete Probability Distributions
Random variables, PMF axioms (0 ≤ p(y) ≤ 1, Σp(y) = 1), and step-wise CDF representation.
PART 1Without Replacement
Example 2: Two Marbles
Two marbles are drawn in succession without replacement from an urn containing 3 red and 2 blue marbles. Let X = number of red marbles. Find the probability distribution.
combinationwithout-replacementhypergeometric
+25 XP
3 stepsPART 1Textbook pg. 88
Example 3.1: Worker Selection
A supervisor has 3 men and 3 women working for him. He chooses 2 workers at random for a special job. Let Y = number of women selected. Find the probability distribution for Y.
combinationhypergeometricsymmetry
+25 XP
3 stepsPART 1Binomial pmf (n=4, p=0.5)
Example 5: CDF Deduction
Given the probability function f(x) = \frac{\binom{4}{x}}{16} for x \in \{0, 1, 2, 3, 4\}: (a) Find the cumulative distribution function (CDF) of the r.v. X. (b) Find f(2) using the CDF.
cdfpmf-relationshipbinomialverification
+30 XP
3 steps