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3 p ax b (22) Z (ax b)3=2 dx= 2 5a (ax b)5=2 (23) Z x p x a dx= 2 3 (x 2a) p x a (24) Z r x a x dx= p x(a x) atan 1 p x(a x) x a (25) Z r x a x dx= p x(a x) aln p x p x a (26) Z x p ax bdx= 2 15a2 ( 2b2 abx 3a2x2) p ax b (27)Z p x(ax b) dx= 1 4a3=2 h (2ax b) p ax(ax b) b2 ln a p x p a(ax b) i (28)Z p x3(ax b) dx= b 12a b2 8aThe probability density function (PDF) of a random variable, X, allows you to calculate the probability of an event, as follows For continuous distributions, the probability that X has values in an interval (a, b) is precisely the area under its PDF in the interval (a, b)4 CS 441 Discrete mathematics for CS M Hauskrecht Equality Definition Two sets are equal if and only if they have the same elements Example • {1,2,3} = {3,1,2} = {1,2,1,3,2} Note Duplicates don't contribute anythi ng new to a set, so remove them The order of the elements in a set doesn't contribute 3 (a+b)^3 formula pdf