|P(X = x) |X(P(X = x) | |0 |0.3 | | |1 |0.2 | | |2 | | | |3 |0.4 | | a. Find the probability that X = 2. b. Find the expected value. Exercise 2 Suppose that you are offered the following “deal.” You roll a die. If you roll a 6‚ you win $10. If you roll a 4 or 5‚ you win $5. If you roll a 1‚ 2‚ or 3‚ you pay $6. a. What
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the honor code pledge printed on your bluebook. No books‚ notes or electronic devices of any kind are allowed. Show all work‚ justify your answers. 1. (25 pts) Suppose events A‚ B and C‚ all defined on the same sample space‚ have the following probabilities: P(A) = 0.22‚ P(B) = 0.25‚ P(C) = 0.28‚ P(A ∩ B) = 0.11‚ P(A ∩ C) = 0.05‚ P(B ∩ C) = 0.07 and P(A ∩ B ∩ C) = 0.01. For each of the following parts‚ your answer should be in the form of a complete mathematical statement. (a) Let D be the event that
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A goes to the first teller‚ B to the second teller‚ and C queues. To standardize the answers‚ let us assume that TA is the length of time in minutes starting from noon until Customer A departs‚ and similarly define TB and TC . (a) What is the probability that Customer A will still be in service at time 12:05? (b) What is the expected length of time that A is in the system? (c) What is the expected length of time that A is in the system if A is still in the system at 12:05? (d) How likely is
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questions. a. Use the multiplication rule to find the probability that the first two guesses are wrong and the third and fourth guesses are correct. That is‚ find P(WWCC)‚ where C denotes a correct answer and W denotes a wrong answer. b. Make a complete list of the different possible arrangements of 2 wrong answers and 2 correct answers‚ then find the probability for each entry in the list. c. Based on the preceding results‚ what is the probability of getting exactly 2 correct answers when 4 guesses
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accessible as possible. The notes should be readable by someone who has taken a course in introductory (non-measuretheoretic) probability. The first part is about Markov chains and some applications. The second one is specifically for simple random walks. Of course‚ one can argue that random walk calculations should be done before the student is exposed to the Markov chain theory. I have tried both and prefer the current ordering. At the end‚ I have a little mathematical appendix. There notes are
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Software Information Folder under Week 0 on Moodle. (a) Use the Excel function NORM.S.DIST to calculate the following probabilities to four decimal places‚ where the random variable Z follows a standard normal distribution. Write your answers to four decimal places on this sheet and remember to draw the curves? For every second question‚ please use your tables to find the probability as well as Excel. (i) P(Z 0.443) (ii) P(Z <1.522) = (iii) P(Z 1.944) (iv) P(0 Z 1.282) (v)
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| Probabilistic techniques assume that no uncertainty exists in model parameters. Answer | | | | | Selected Answer: | False | Correct Answer: | False | | | | | Question 5 2 out of 2 points | | | P(A | B) is the probability of event A‚ if we already know that event B has occurred. Answer | | | | | Selected Answer: | True | Correct Answer: | True | | | | | Question 6 2 out of 2 points | | | A continuous random variable may assume only
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level. Calculate the probability that not more than one high acidity level catalyst is selected. [4 marks] b) Potholes on a highway can be a serious problem and are in constant need of repair. With a particular type of terrain and make of concrete‚ past experience suggests that‚ on the average‚ 2 potholes per kilometre after a certain amount of usage. It is assumed that the Poisson process applies to the random variable for the number of potholes. i. What is the probability that there will be between
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Hai------------------------------------------------- 3. a) What is the probability that none of these vehicles requires warranty service? ------------------------------------------------- P(x=0) = 12 C0 (0.10)0 (1-0.10)12-0 ------------------------------------------------- = (1) (1) (0.28243) ------------------------------------------------- =0.28243 ------------------------------------------------- b) What is the probability that exactly nine of these vehicles require warranty service? -------------------------------------------------
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PROBABILITY P(A U B)= P(A) + P(B) – P(A∩B) If P(A∩B) = 0 then A and B are mutually exclusive and P(AUB) = P(A) + P(B) Joint Probability Marginal Probability PXY(x‚y) = P(X=x ∩ Y=y) PX(x) = ∑P(X=x ∩ Y=y) (For all values of y) Quotient Rule: Multiplication Rule P(A|B) = P(A∩B) / P(B) P(A∩B) = P(A|B) x P(B) = P(B|A) x P(A) Two events are statistically independent if: P(A|B) = P(A) P(B|A) = P(B) P(A∩B) = P(A) P(B) _ _ P(A) = P(A|B)P(B) + P(A|B)P(B) Bayes Rule:
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