Collection of problems in probability theory by L.D. Meshalkin

By L.D. Meshalkin

The Russian model of a set of difficulties in chance thought includes a bankruptcy dedicated to records. That bankruptcy has been passed over during this translation simply because, within the opinion of the editor, its content material deviates a bit from that that is recommended by means of the name: difficulties in seasoned­ bability concept. the unique Russian model includes a few mistakes; an try out used to be made to right all blunders came across, yet might be a number of stiII stay. An index has been additional for the benefit of the reader who might be looking for a definition, a classical challenge, or no matter what. The index lists pages in addition to difficulties the place the listed phrases seem. The publication has been translated and edited with the wish of leaving as a lot "Russian style" within the textual content and difficulties as attainable. Any pecu­ liarities current are probably as a result this purpose. August, 1972 Bryan A. Haworth viii Foreword to the Russian version This choice of difficulties in likelihood concept is essentially meant for college scholars in physics and arithmetic departments. Its target is to assist the scholar of likelihood concept to grasp the speculation extra professional­ foundly and to acquaint him with the applying of chance conception how you can the answer of sensible difficulties. This assortment is geared primarily to the 3rd version of the GNEDENKO textbook direction in proba­ bility conception, Fizmatgiz, Moscow (1961), chance concept, Chelsea (1965).

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B) What is the probability that of 10 points located at random independently of each other in the interior of the circle, four fall into the square, three on one segment and one each on the remaining three segments? 106. 2 for each individual shot. One hit is sufficient to destroy. What is the probability of destruction with 2 shots? What is the probability of destruction with 10 shots? 107. For a certain competition, each of the athletic leagues A and B picks three teams. 4. Find the probability that league A wins at least two games of the three.

Find the expectation and dispersion of: a) (1 =~-211; b) (2=2~-11. D[~J=I, 151. Assume that in a lake there were 15,000 fish, 1000 of them marked [with radioactive tracers] (see Problem 100). 150 fish were fished out of the lake. Find the expectation of the number of marked fish among the fish caught. 152. Find the expectation and the dispersion of the number of short fibers among the randomly selected fibers in Problem 94. 153. In throwing n dice, determine the expectation, the dispersion, and central moment of the 3-rd order of the sum of the eyes on all dice.

F. F~l'"'' ~JXI'"'' xn)=Pg l

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