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Discussion Slides 1: Discrete Random Variable for EEE 137
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Probability Theory Probability quantitative measure of how “likely” a certain event will occur Axioms of Probability AXIOM I: 0 <= P [A] <= 1 AXION II: P [S] = 1 AXIOM III: If A ∩ B = 0, P (A ∪ B) = P (A) + P (B)
DEFINITION: Random Variable (RV) A function that associates a unique numerical value with every outcome of an experiment. A Random Variable can be either Discrete or Continuous. Discrete: a number obtained by counting i.e. Number of students present today Continuous: a number obtained by measuring i.e. Weight of students in this class
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The Experiment Marksman keeps shooting until target is hit. Sample Space Discrete (half a hit is impossible) X ∈ {1, 2, 3, 4, 5, … } Problem 1: The Marksman ? ? ? ?
DEFINITION: Independence Two Events A and B are INDEPENDENT if and only if their joint probability equals the product of their probabilities. i.e. P (A ∩ B) = P(A) x P(B)
To get the CDF, just sum all probabilities prior to the current value Problem 1: The Marksman 1 2 3 4 5 6 7 8...
1 Note that this is an increasing function!
What is the probability that the marksman will hit the target after at most 10 shots? P (X=n) = (miss) n- 1 x (hit) PX(X=x) = (0.9) x- 1 x (0.1) Problem 1: The Marksman 1 2 3 4 5 6 7 8...
F(X=10) = 0. Note: This problem constitutes a Geometric Random Variable
Quiz: The Marksman
Profit = Revenues - Cost = 55 (0.5) X
Additional Reading Material Discrete and Continuous Random Variables http://www.henry.k12.ga.us/ugh/apstat/chapternotes/7supplement.html
