Lecture8_DiscreteRVs

Lecture8_DiscreteRVs - ECE 340 Probabilistic Methods in...

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ECE 340 Probabilistic Methods in Engineering M/W 3-4:15 Prof. Vince Calhoun Prof. Vince Calhoun Lecture 8: Discrete RVs Lecture 8: Discrete RVs
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Review of Jean’s Lectures • Independence (2.5-2.6) • Counting/Conditional Probability (3.1-3.2) • Expected Value (3.3) • Conditional PMF/Conditional EV (3.4)
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Reading • This class: Section 3.5 • Next class: Section 4.1-4.3
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Outline • Section 3.5 • Discrete RV’s • Examples • Bernoulli • Binomial • Geometric • Poisson
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Bernoulli Distribution i. A Bernoulli experiment is a random experiment of which outcomes can be classified as one of 2 values. Success or failure; male or female; defective or non- defective. ii. Bernoulli Distribution: p(x) = f(x) =p x (1-p) 1-x , x = 0, 1 iii. This is a p.m.f, which describes a r.v. X which follows the Bernoulli distribution. This Bernoulli Distribution r.v. X has an associated mean & variance. μ = E[X] = Σ xp(x) = Σ xp x (1-p) 1-x = (0)(1-p) + (1)(p) = p σ 2 = V(X) = Σ (x – p) 2 p x (1-p) 1-x = p 2 (1-p) + (1-p) 2 p = p(1 – p) = pq
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Binomial Distribution i. Note: We are only interested in the total # of successes and NOT in the order of those successes. Order is irrelevant. ii. If we let the r.v. X equals to the number of observed successes in n Bernoulli Trials, the possible values of X are 0, 1, 2, …, n.
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Lecture8_DiscreteRVs - ECE 340 Probabilistic Methods in...

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