Econ 1701 Tuesday November 29th 2019.docx - Econ 1701:...

Econ 1701: Tuesday, November 29th, 2019
Probability distribution for continuous random variables:
- If RV is discrete can assign a probability to each value x takes on
- Continuous takes on an infinite number of values
- i.e. takes on fraction values
- All points on continuous line interval
- Can't assign a probability to each of infinite values
- If take measurements on a continuous random variable will get narrow class bands
- More observations → narrower class bands
- f(x) = probability density function
Properties of continuous probability density functions
- Area under curve adds up to 1
- P(a≤x≤b) = area under the curve between a and b
- Probability that x = a P(x=a) = 0
- P(x≤a) = P(x<a)
- P(x≥a) = P(x>a)
- Need continuous function f(x) that describes the model
- Pick model that best fits the data and allows you to make inferences
- Uniform distribution
- Random variable is evenly distributed over an interval
- Ex. Old faithful geyser
- Erupts every 91 minutes
- If arrive at random time and wait 20 minutes what is probability will see an
eruption
- P(a ≤ x ≤ a+20)
- Exponential distribution
- Use for wait timea or life times
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