Umm Al-Qura University بسم الله الرحمن الرحيم Umm Al-Qura University Health Sciences College at Al-Leith Department of Public Health Lecture (6)

Probability Distributions statistic

Objectives: 1/ Define basics of Probability Distributions. 2/ Define Types of Probability Distributions. 2/ Give an Example of Probability Distributions.

The Binomial Distribution Discrete statistic

The Binomial Probability Distribution p = P(S) on a single trial q = 1 – p n = number of trials x = number of successes statistic

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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? statistic

The Binomial Distribution Mean Variance Standard Deviation statistic

Bernoulli Distribution Discrete statistic

Bernoulli Distribution it special case from Binomial Distribution ( n =1) f(x) = px (1-p)1-x,    for x = 0, 1 μX = E(X) = np = p n=1 μX =p σ2X = Var(X) = np(1−p) n=1 σ2X = Var(X) = p(1−p) statistic

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 statistic

Normal Distribution Continuous statistic

X ~ N(μ,σ2) statistic

Calculating Probabilities for Standard Normal Distribution statistic

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 ? statistic

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