A modern introduction to probability and statistics : by F M Dekking; et al PDF

By F M Dekking; et al

ISBN-10: 1852338962

ISBN-13: 9781852338961

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3 is often useful to compute the probability of the union of two events. What would be the corresponding rule for three events A, B, and C? It should start with P(A ∪ B ∪ C) = P(A) + P(B) + P(C) − · · · . 1. 16 Three events E, F , and G cannot occur simultaneously. Further it is known that P(E ∩ F ) = P(F ∩ G) = P(E ∩ G) = 1/3. Can you determine P(E)? 15 then it seems that you do not have enough information; make a diagram instead. 17 A post office has two counters where customers can buy stamps, etc.

There are six permutations of the numbers 2, 5, and 8 (see page 14). Thus, compensating for this six-fold overcount, the number C10,3 of ways to correctly answer 3 questions out of 10 becomes C10,3 = 10 · 9 · 8 . 3·2·1 More generally, for n ≥ 1 and 1 ≤ k ≤ n, Cn,k = n(n − 1) · · · (n − (k − 1)) . k(k − 1) · · · 2 · 1 Note that this is equal to n! , k! (n − k)! which is usually denoted by nk , so Cn,k = nk . Moreover, in accordance with 0! = 1 (as defined in Chapter 2), we put Cn,0 = n0 = 1. 5 Show that Substituting 10 k n n−k for C10,k we obtain = n k .

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A modern introduction to probability and statistics : understanding why and how by F M Dekking; et al


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