Download An Introduction to Probability and Statistics (Wiley Series by Vijay K. Rohatgi, A.K. Md. Ehsanes Saleh PDF

By Vijay K. Rohatgi, A.K. Md. Ehsanes Saleh

The second one variation of a well-received publication that used to be released 24 years in the past and keeps to promote to this present day, An advent to chance and information is now revised to include new info in addition to gigantic updates of present fabric.

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Extra info for An Introduction to Probability and Statistics (Wiley Series in Probability and Statistics)

Example text

Thus, if a point is chosen at random from the interval (a, b), the probability that it lies in the interval (c, d), a s c < d S b, is (d-c)f(b-a). Moreover, the probability that the randomly selected point lies in any interval of length (d - c) is the same. We present some examples. Example 6. A point is picked "at random" from a unit square. Let n = { (x, y) : 0 s x s 1, 0 :<:: y :<:: I } It is clear that all rectangles and their unions must be in . 0 ) ------.. ;... l. A= {(x,y): 0 :S x :S �.

And !. are not independent. Now consider families with three children. Assuming that each of the eight pos­ sible gender distributions is equally likely, we have P(E) = �. P(F) = i. and i. P(EF) = so that E and F are independent. An obvious extension of the concept of independence between two events A and B to a given collection 11 of events is to require that any two distinct events in 11 be independent. Definition 2. Let 11 be a family of events from S. We say that the events U are painvise independent if and only if for every pair of distinct events A, B E 11, P(AB) = PA PB.

L. A= {(x,y): 0 :S x :S �. � :S y :S I}. S; so, too, should be all circles in the unit square, since the area of a circle is also well defined. Indeed, every set that has a well-defined area has to be inS. We choose S = �2. the Borel a -field generated by rectangles in Q. As for the probability assignment, if A E S, we assign P A to A, where PA is the area of the set A. If A = ( 1, {(x, y): 0 :::; x :::; �.! 1) and radius ! , then P B :::; y = rr :::; l}, then (! -If B is a circle with center = rr I4.

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