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continous probability notes

continous probability notes - 1 f(x = 3e-3x for...

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Probability for Continuous Random Variables X is called a “continuous” random variable if the possible values of X consist of all the real numbers on some interval of the real numbers. In this case, X has a probability density function (often denoted pdf) of the form f(x), where 1. f(x) is always greater than or equal to zero (and it is non-zero only for the possible values of the random variable X) 2. the integral of f(x), ∫f(x)dx = 1, where this integral is over the whole real line, -∞<x<∞. (Of course, if f(x) is zero over big parts of this range then the integral may in practicality, look like an integral over a smaller region.) examples
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Unformatted text preview: 1. f(x) = 3e-3x for 0≤x<∞ and 0 elsewhere verify 2. f(y) = (1/12)[4+2y-y 2 ] for 0≤y≤3 and 0 elsewhere verify In this situation, we have probabilities for intervals of values, but assume that the probability of any individual point is 0. 1. in number 1 above P[.1≤X≤.4] P[X>.5] P[X=3] = 0 2. in number 2 above P[0<Y<1] P[Y>.5] The expected value of a continuous random variable is the average value that you would get if you observed the random variable many (infinitely many) times. E[X] = ∫xf(x)dx, where the integral is over the range of possible values of the variable X. Examples from above continous probability...
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