By F M Dekking; et al
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Extra info for A modern introduction to probability and statistics : understanding why and how
2 A fair die is thrown twice. ” a. Calculate P(A | B). b. Are A and B independent events? 3 We draw two cards from a regular deck of 52. ” a. Compute P(S1 ), P(S2 | S1 ), and P(S2 | S1c ). b. Compute P(S2 ) by conditioning on whether the ﬁrst card is a spade. 10. 3 · 10−5 . Compute P(B | T ) and P(B | T c). 5 A ball is drawn at random from an urn containing one red and one white ball.
3..... ... ...... 1 ....... .. . . ... .... ... ... ... ..... ..... .. 2 ......... . . . ....... ... .......... ......... ... ... 3 ... .... . ... . 1 ... ... ... 2 ... ... . ... A C A∩C C A∩C A∩C A∩C A∩C C C C Ω Fig. 2. The law of total probability (illustration for m = 5). 2). Another, perhaps more pertinent, question about the BSE test is the following: suppose my cow tests positive; what is the probability it really has BSE?
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 . 48 4 Discrete random variables P(X = k) = 10 k 1 4 k 3 4 10−k . Since P(X ≥ 6) = P(X = 6) + · · · + P(X = 10), it is now an easy (but tedious) exercise to determine the probability that you will pass. 0197. It pays to study, doesn’t it?! The preceding random variable X is an example of a random variable with a binomial distribution with parameters n = 10 and p = 1/4. Definition. A discrete random variable X has a binomial distribution with parameters n and p, where n = 1, 2, .
A modern introduction to probability and statistics : understanding why and how by F M Dekking; et al