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The pdf f x gives us the probability that the random

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Unformatted text preview: , we can just add up the frequencies of all the bins in this interval and divide it by the population size. The pdf, f (x), gives us the probability that the random value falling into the extremely small neighborhood around any particular value x. Remark. Suppose that a random variable X has a probability density function f (x), then the probability of the particular event that the random variable X falls into some interval [x1 , x2 ], P rob(x1 < X ≤ x2 ), is measured by the area below the density function and bounded by the interval [x1 , x2 ]. Notice that when describing the probabilities of a continuous random variable, we measure the probability of a certain event in an “incremental” manner. 28 EC 271 Applied Statistical Methods: Lecture Notes (Leshui He) 2014 Therefore a higher density at certain outcome value x means that the probability of this random variable X lying close to x is higher. 3.2 3.2.1 Normal Distribution (Gaussian Distribution) Probability Distribution Function (pdf ) of Normal Distribution The probability density...
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