Transcription of Examples of Continuous Probability Distributions
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Examples of Continuous Probability Distributions
Examples of Continuous Probability Distributions :The normal and standard normalThe Normal DistributionXf(X)Changing shifts the distribution left or increases or decreases the Normal Distribution:as mathematical function (pdf)2)(2121)( =xexfNote constants: = is a bell shaped curve with different centers and spreads depending on and The Normal PDFIt s a Probability function, so no matter what the values of and , must integrate to 1!1212)(21= + dxex Normal distribution is defined by its mean and standard dev. E(X)= = Var(X)= 2 =Standard Deviation(X)= dxexx + 2)(2121 2)(212)21(2 + dxexx**The beauty of the normal curve: No matter what and are, the area between - and + is about 68%; the area between -2 and +2 is about 95%; and the area between -3 and +3 is about Almost a
The “probnorm(Z)” function gives you the probability from negative infinity to Z (here 1.5) in a standard normal curve. The “probit(p)” function gives you the Z-value that corresponds to a left-tail area of p (here .93) from a standard normal curve. The probit function is also known as the inverse standard normal function.
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