The probability that a soldier in particular region will be infected by a particular typeof hepatitis is 1/800. There are presently 5000 British soldiers in this region. Find(approximately) the probability that at most 10 of the British soldiers will be infectedby this type of hepatitis. (Assume that a soldier can get infected independently of theother soldiers.) Use a Poisson approximation.0.5830.6740.9860.0140.946

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Answered: The probability that a soldier in…

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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You study a population and are interested in the proportionpthat has a certain characteristic. You are unaware that this proportion of the population isp=0.67. You have taken a random sample of sizen & 129of the population and determined that the proportion of the sample having the characteristic isp=0.73. His sample is Sample 1 in the following table. (In the table, Sample 1 is indicated by "M1", Sample 2 by "M2", and so on). (to) Based on Sample 1, plot the confidence intervals of80%and of95%for the population proportion. Use1,282for the critical value for the confidence interval of80%, and use1960 for the critical value for the confidence interval of95%. (If necessary, you can refer to a list of formulas.) • Write the upper limit and the lower limit on the graphs to indicate each confidence interval. Write the answers with two decimal places. • For the points ( ♦and ◆), write the population proportion,0.67. 0.47 0.47 80% confidence interval 0.65 X 0.84 0.84 0.47 0.47 95% confidence…
Please answer page 143, 2.6.6.
85% of tax returns have computational errors. This means that if we randomly select a tax return, there is a probability of 0.85 that the tax return will have at least one computational error. Whether one tax return has a computational error is independent of whether any other tax return has a computational error. John Jay, a new tax return auditor randomly selects tax returns for audit one after another. Let X = the number of tax returns selected until he selects the 1st return with computational errors. Let Y = the number of tax returns selected until he selects the 2nd return with computational errors. What is the probability that the 1st 3 tax returns selected have computational errors? What is the expected value of X? What is the variance of X? What is the probability that X > 3? What is the probability that X < 3? What is the probability that Y = 4? What is the probability that Y< 4?
Assume that 1 out of every 5 adults in a local community is unemployed. Approximatethe probability that in a random sample of 100 adults from the community, more than 25are unemployed. Express your final answer in terms of the standard normal cumulativedistribution function Φ.
Question 3: Discrete random variables Each bit transmitted through a channel has a 10% chance to be transmitted in error. Assume that the bits are transmitted independently. Let X denote the number of bits in error in the next 18 transmitted bits. Answer the following questions a) Find the probability that in the next 18 transmitted bits, at least 3 transmitted in error. b) Calculate the expected value, variance and standard deviation of X. c) Find the probability that X is within 1 standard deviation of its mean value.
Suppose that in a certain small town it either rains or is sunny every day. A meteorologist notes that when it is sunny in this town, it will be sunny the next day with probability 0.3. If it rains, it will be sunny the next day with probability 0.4. Answer the following questions:
A QR code photographed in poor lighting, so that it can be difficult to distinguish black and white pixels. The gray color (X) in each pixel is therefore coded on a scale from 0 (white) to 100 (black). The true pixel value (without shadow) the code is Y = 0 for white, and Y = 1 for black. We treat X and Y as random variables. For the highlighted pixel in the figure is the gray color X = 20 and the true pixel value is white, i.e. Y = 0. We assume that QR codes are designed so that, on average, there are as many white as black pixels, which means that pY (0) = pY (1) = 1/2. In this situation, X is continuously distributed (0 ≤ X ≤ 100) and Y is discretely distributed, but we can still think about the simultaneous distribution of X and Y. We start by defining the conditional density of X, given the value of Y : fX|Y(x|0) = "Pixel is really white" fX|Y(x|1) =" Pixel is really balck " Use Bayes formula as given in the picture and find the probability for x = 20 like in the picture.
Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
Find P(X = 3) if the mean of the Poisson random variable is A = 10. O 0.007567 O 0.004540 O 0.000067 0.271801
Chapters: Normal and Exponential random variables. Q: There exist naturally occurring random variables that are neither discrete nor continuous. Suppose a group of people is waiting for one more person to arrive before starting a meeting. Suppose that the arrival time of the person is exponential with mean 4 minutes, and that the meeting will start either when the person arrives or after 5 minutes, whichever comes first. Let X denote the length of time the group waits before starting the meeting. - a. Find P(0
5. Suppose that a student attending a class has an infectuous disease. Suppose that with probability 1/2 she does not infect anybody, with probability 1/4 she infects exactly one other person, and with probability 1/4 she infects exactly two people. Let X be the number of people infected by this student. Calculate the expectation and the variance of X.
What does the memoryless property refer to? An event cannot occur if it has already occured within a recent specified time period. The distribution of the time until an event does not depend on how much time has already passed. The occurrence of an event is independent of the number of times that event has already occurred. None of the above.

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