‫بسم هللا الرحمن الرحيم‬
Umm Al-Qura University
Health Sciences College at Al-Leith
Department of Public Health
Lecture (6)
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Objectives:
1/ Define basics of Probability Distributions.
2/ Define Types of Probability Distributions.
2/ Give an Example of Probability Distributions.
The Binomial Distribution
Discrete
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
The Binomial Probability Distribution
p = P(S) on a single trial
 q = 1 – p
 n = number of trials
 x = number of successes

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 n  x n x
P( x)    p q
x
 
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

Say 40% of the class is female.
What is the probability that 6 of the first 10
students walking in will be female?
 n  x n x
P ( x)    p q
 x
10  6 106
  (.4 )(. 6 )
6
 210(.004096)(. 1296)
 .1115
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The Binomial Distribution
Mean
Variance
Standard Deviation
  np
  npq
2
  npq
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Bernoulli Distribution
Discrete
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Bernoulli Distribution it special case from
Binomial Distribution ( n =1)
f(x) = px (1-p)1-x,
μX = E(X) = np = p
n=1
μX =p
for x = 0, 1
σ2X = Var(X) = np(1−p)
n=1
σ2X = Var(X) = p(1−p)
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Coin , p(H) = 0.4 and p(T) = 0.6
Find
X ~ Bernoulli (0.6)
μX =p = 0.6
σ2X = Var(X) = p(1−p) = 0.6*0.4 = 0.24
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Normal Distribution
Continuous
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X ~ N(μ,σ2)
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Calculating Probabilities for Standard Normal Distribution
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If the length of one of the tribes are distributed naturally by
average (165cm) and standard deviation (5cm) Find the standard
value (z), where x= 172 , and value (x) if z= -0.52 ?
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