By Lionel Porcheron

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2. Now it is clear that the values of X are not equally likely. 2: Histogram for sum of two equally likely numbers, both chosen in interval [0,1]. to be much more probable. Hence, we have generated a "counterexample" to the proposed theorem, or at least some evidence to the contrary. We can build up our intuition by continuing with our experimentation. Attempting to justify the observed occurrences of X, we might suppose that the probabilities are higher near one because there are more ways to obtain these values.

2;. 10. 7 for the true PDF). 5. 10: Estimated PDF of X^ for X Gaussian. 3. 11. 11: Estimated and true mean. 5 - Multiple random variables Consider an experiment that yields two random variables or the vector random variable [Xi X2]-^, where T denotes the transpose. An example might be the choice of a point in the square {(x^y) : 0 < x < 1,0 < y < 1} according to some procedure. This procedure may or may not cause the value of X2 to depend on the value of xi. 12a, then we would say that there is no dependency between Xi and X2.

A set is defined as a collection of objects, for example, the set of students in a probability class. 1) or by the description method A = {students: each student is enrolled in the probability class} where the ":" is read as "such that". } (enumeration) B = {/ : J is an integer and / > 1} (description). 2) Each object in the set is called an element and each element is distinct. For example, the sets {1,2,3} and {1,2,1,3} are equivalent. There is no reason to list an element in a set more than once.

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Maple, cours et applications by Lionel Porcheron
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