Questions and Answers of Probability And Stochastic Modeling

An urn has b black and r red balls. A ball is drawn and put back into the urn together with c balls of the same color. (So, now there are b+r+c balls in the urn.)After that again a ball is
A systems consist of components configured as shown in Fig. 6b; pi is the probability that component i works; the components function independently. Find the probability that a signal will go
Two friends are fishing on a river and their time is limited. For each, the probability of catching a fish is p < 1. The probability that somebody will catch two fish is zero and the results of
A transmitter is receiving a digital text, i.e., a sequence of digits. Suppose that each digit in the sequence is equally likely to be any number from 0 to 9, and the digits are appearing
Consider the Bayes framework of Section 2.6. Suppose that an event A concerns the result of the experiment, and we know that P(AB1) > P(AB2). Given A, which hypothesis is more probable: B1 or B2?
On the average, out of 100 people who are taking a professional exam, twelve took a special tutoring course that increases the percentage of passing the exam from 70% to 90%. Ms. K has passed the
Give a heuristic explanation why the ruin probability in (2.4.5) must be smaller than in (2.4.7). Double check it using simple algebra. qu - 1-pa (2.4.5)
There are two groups of students. The first consists of ten males and eleven females; the second consists of five males and six females. Two representatives, one from each group, were chosen at
A country is divided into three provinces with 40%, 35%, and 25% of the total population.Due to climate conditions, in the first province, 55% of the people are interested in gardening, while in the
In Example 2.4-1, the probability p9 ≈ 0.66 and is larger than 0.4, the probability to “move up.” Explain this from a heuristic point of view.
Consider the situation of Example 3-1. Let An be the event that the nth trial is successful, Bn be the event that the first success occurred in the nth trial, and A be defined as in Section 3. (a)
Problems below concern the model of Section 2.4 with a = ∞.(a) For a separate moment of time, the odds are 3 to 1 in favor of gains. Which initial capital should company start with for the ruin
For a sequence of events An such that P(An)→0, should P(An occur infinitely often) = 0?
Can we apply the Borel-Cantelli theorem for one or two games of heads and tails?
Consider an infinite sequence of trials with probabilities of success perhaps depending on the numbers of the trials.(a) Can the number of successes be finite with probability 0.5 if the trials are

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