# Homework5

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1. Bernoulli Distribution:

Parameters: p = prob. of success = (0 ≤ p ≤ 1)
Range = x {0,1}

Probability mass function f of this distribution is:
f(x) = 1-p if x = 0 ; p if x = 1 ; 0 otherwise
• Mean = p
• Variance = p (1-p)
2. Binomial Distribution:

Notation: B(n,p)
Parameters: p = 0 < p < 1 (+integer)
n = numer of trials = n > 0
Range = x={0,1,...n}

Probability mass function (pmf) is:
﻿﻿(n/p) pk (1-p)n-k

• Mean = np
• Variance = np (1-p)
3. Exponential Distribution:

*x = t ; 1/a = delta

Parameters: a = (1/x) sacale parameter
Range = x= {0 ≤ x ≤ ∞}
Pmf = f(x) = 1/a * e-x/a

• Mean = delta-1 or 1/delta *delta = λ
• Variance = delta-2 or (1/delta)2 = (1/λ)2
4. Geometric Distribution:
Parameter: p = probability of success = (0 < p < 1)
Range: x = { 1,2,3…∞}
Probability mass function (pmf) is:
f(x) = (1-p)x-1 p
• Mean = 1/p
• Variance = (1-p)/ p2
5. Poisson Distribution:

Notation: Pois(λ)
Parameter: λ = mean ; λ >0
Range: x = {0, 1, 2, 3, …, ∞}
Probability mass function (pmf) is:

k / k!) * e

• Mean = λ
• Variance = λ

### Card Set Information

 Author: erika01 ID: 111831 Filename: Homework5 Updated: 2011-10-24 21:55:55 Tags: Kumar CNP Folders: Description: Problems and Solutions Show Answers:

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