CHAPTER 4: CONTINUOUS RANDOM VARIABLES & PROBABILITY DISTRIBUTIONS
4 CONTINUOUS RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 4.1 CONTINUOUS PROBABILITY DISTRIBUTIONS •
A continuous r.v is all possible value that can be assumed in the possible range of the r.v where the data can take infinitely many values
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Example of continuous r.v: Time in second required to process certain program Time for baby to gain weight Amount of rainfall in certain city
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The probability function of continuous r.v is called probability density function (pdf)
4.1.1 PROBABILITY DENSITY FUNCTION (PDF) The function f(x) is a probability density function (pdf) for the continuous r.v. X, defined over the set of real number if 1)
f ( x) ≥ 0 for − ∞ < x < ∞
2)
∫
3)
P(a ≤ x ≤ b) = P(a ≤ x < b) = P(a < x ≤ b) = P(a < x < b) = ∫a f ( x)dx
∞
−∞
f ( x)dx = 1 b
Note: The probability can be interpreted as area under the graph between the interval from a to b
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