14:21. It is known from past experience that in a certain p!ant there are on the average 4industrial accidents per month. Find the probability that in a given year there will be less than 4 accidentsAssume Poisson distribution. (e 4= 0-0183)will a

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A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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III on a particular lamp post, the bulb is replaced as soon as it gets busted. Let the total number of replacements Nt up to time t have a Poisson distribution w/ intensity a=.02 replacement per day. Consider the bulb working on the 60th day. 1. Find the probability that it gets buuted in 15 days or less. 2. Find the probability that it is functioning for more than 10 days already.
7 If X has Poisson distribution with mean 6. what is P(X-7)? Select one: ut of a. 138 b. None of them C. 0.318 d. 0.681 e. 0.138 as page CS Scanned with CamScanner
4.6. Consider the following history of six events in which operations span multiple ob- jects, assuming that A and B are initialized to 0: ev = inv(write(1)) on evz = inv(sum() evy = resp(urite()) from A evA = inv(write(2)) on evs = resp(write()) from B evg = resp(sum(2)) from A, B at P at P А, В at Pa at P at P at Ps A on B Show that this history is not linearizable but normal.
4.1 Let X have a geometric distribution, that is p(x) = q*-'p x = 1,2,3, .. Where X has the memoryless property given by: P(X > k + b|X > k) = P(X > b). Given that you have already tossed a balanced coin 5 times and obtained Zero heads, what is the probability that you must toss it at least 3 more Times to obtain the first head?
12. The number of new individuals in a population of animals is sometimes approximated calculating the expected number of survivors of the new born animals from the next genera- tion. The idea is that the number of new animals born follows some probability distribution, and the number of animals that survive depend on how many are present.¹ One example of a survivor function is the following: S₁(k) = b.ck, where b and c are real numbers with 0
3. 4-5 Please solve the following with the provided information
7-10. Suppose that the random variable X has the continu- ous uniform distribution f(x) = = [1, 0≤x≤1 10, otherwise Suppose that a random sample of n = 12 observations is selected from this distribution. What is the approximate probability distribution of X- 6? Find the mean and vari- ance of this quantity.
8. The time (in minutes) that it takes a car mechanic to replace a car battery is a random variable X that follows an exponential distribution with mean 15 minutes. a) Find P(14 < X < 22). Round off your answer to two decimal places. x 22 1 P(14 < X <22) = √₂/1² 15 e 15dx = P(x < 22) — P(x < 14) x 15 122 = e 15 22 1 - e 14 or 0.8 = = 22 14 = −e 15 + e15 = 0.16254≈ 0.16 - (1 – b) Find the 80th percentile. Round off to the nearest whole number. 1 X S 15 14 e 15 t e 15 dt X 0.8 = 1 e 15 X e 15 = = 0.2 14 22 = e 15 e 15 = 0.16 x — = ln (0.2). This gives x = 24.14156 15

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14-21. It is known from past experience that in a certain p!ant there are on the average 4 ndustrial accidents per month. Find the probability that ina given year there will be less than 4 accidents Assume Poisson distribution. (e 4 0-0183)