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9FA4 - Econ 180 Assignment 4 Continuous Random Variables...

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Econ 180. Assignment 4. Continuous Random Variables: Normal Distribution. 1. Def: The continuous probability distribution is the probability distribution of a continuous random variables (X). It can not be presented in tabular form, but it can be presented by a formula. Such a formula would necessarily be a function of the numerical values of the continuous variable X as such could be graphed as a smooth curve . The probability function portrayed by this curve is called probability density function (pdf), a frequency distribution, or a probability distribution. 2. Def: Probability density function (pdf): Let X be a continuous random variable, and x be any lying in the range of values this random variable can take. pdf, f(x) of the random variable is a function with the following properties: (1) The area under its curve and above the x axis is equal to 1, i.e., ⌠ f(x)dx = 1. -∞. (2) The area under the curve between two ordinates x = a and x = b with a < b gives the probability that x lies between a and b, i.e., p(a ≤ x ≤ b) = p(a < x < b).
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