chapter 8 (2)

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ECON1203 - StatisticsChapter 8 – Continuous probability distributions ECON1203 – Statistics Chapter 8 – Continuous probability distributions 1 Probability density functions Requirements of probability density functions 1. f ( x ) 0[ wherea≤x≤b] 2. The area under f ( x ) between a and b is 1 a b f ( x) dx =1 2 Uniform probability distribution (rectangular probability distribution) f ( x )= 1 ba [ wherea≤x≤b] P ( x 1 < X< x 2 ) =Base ×Height= ( x 2 x 1 ) × ( 1 ba ) 3 Normal distribution f ( x )= 1 σ 2 π e 1 2 ( xμ σ ) 2 [ where<x < ] 1. It is symmetric about the mean ( μ) . 2. Increasing the standard deviation ( σ ) widens the function. Page 1 of 6

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chapter 8

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ECON1203 - StatisticsChapter 8 Continuous probability distributionsECON1203 StatisticsChapter 8 Continuous probability distributionsProbability density functionsRequirements of probability density functions1. 2. The area under between and is Uniform probability distribution (rectangular probability distribution)

Normal distribution

1. It is symmetric about the mean .2. Increasing the standard deviation widens the function.Normal probabilities3. 4. 5.

Finding values of 6. 7. Excel Exponential distribution

1. Increasing the parameter of distribution steepens the function.2. Probabilities3. 4. 5. Excel6.

Student distribution

1. 2. 3. It is symmetric about zero .4. It is flatter than standard normal distributions.5. Increasing the degrees of freedom narrows the function.Probabilities 6. 7. Excel8. 9. 10. Chi-squared distribution

1. Increasing the degrees of freedom flattens the function.2. 3. Probabilities4. 5. Excel6. 7.

distribution

1. 2. Probabilities3. 4. Determining values of 5.

6. 7.

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