Problem 1quested quantities.(~)143in5 1/21 Co olla 14.IIa(d) Let = {1, 2, 3, 4, 5]. Assume that P[{1}] = 0.1, P[{2}]ΩP[{3, 4, 5}]?=DIDetermine each of the re-Wat i-1/0.0.2, and P[{3}]and= 0.2. What is(e) In Metropolis, the probability that a random citizen has Covid is 0.1 (determined via high-quality surveillance testing). LexCorp is selling a test that returns false negatives withconditional probability 0.2 and false positives with conditional probability 0.05. Given thata citizen tests negative, what is the conditional probability that they actually have Covid?If a citizen tests positive, what is the conditional probability that they actually have Covid?

We will use the concepts of the probability to obtain the results in both the questions.

Answered: (d) Let N = {1, 2, 3, 4, 5}. Assume…

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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Studies show that some people who are fully vaccinated against COVID-19 will still getsick. Suppose that out of 10,000 people who are fully vaccinated, an average of one personwill get sick. ii. The probability that at leastrperson get sick is 0.2642. What is the value ofr ?
Suppose that the rats on the campus of Hypothetical U are found to be carriers of bubonic plague. Eradicating the rats has an estimated cost of $1,000,000 and is expected to reduce the probability a given student dies of the plague from 1/3,000 to zero. Suppose that there are 30,000 students on campus. Suppose further that the administration refuses to eradicate the rats due to the cost. From this information, we can estimate that the administration's willingness to pay to save a student statistical life is no more than $100,000 $1,000,000 $50,000 $33,333
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.
Let X1, X2,..., X3 denote a random sample from a population having mean u and variance o?... Which of the estimators have a variance of 7 X1+X2++X, 7 2X1-X6+X4 2 3X1-X3+X4 2 2(X1+X2+.+X¬) 4 7
b. Let X1, X2, X3, and X4 represent the weight of shipment packages at a certain shipment facility. Suppose they are independent normal random variables with means H1 = 3.6, 42=0.9, 3= 1.8, 4 = 7.4 pounds and variances o = = = Find P (2X₁ + 1X2 + 3X3 + 1X4 ≤ 17.6). = 1.
Suppose that each time Bar-bie throws a dart, she has a 3/4 probability of getting a bullseye. If Barbie shoots three darts, what is the probability that she gets a bullseye on at least two of them?
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.
Example 2.3.8 Six dissimilar (distinguishable) balls are distributed at ran- dom into 3 boxes. Find the probability that these boxes contain 3, 2 and 1 balls respectively.
According to recent reports, currently 39% of the population of NC (adults and children) has been fully vaccinated against Covid. Suppose of random sample of 400 individuals from the population of NC is selected. Let x represent the number in the sample who are fully vaccinated. d. Find the probability that 130 or fewer in the sample have been fully vaccinated. Round to 4 decimal places. Would this result be unusual? Explain.
1. If a random variable X takes the value 1,2,3,4 suchthat 2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4).Find the probability distribution of X.
An ordinary (fair) coin is tossed 3 times. Outcomes are thus triples of "heads" (h) and "tails" (t) which we write hth, ttt, etc. For each outcome, let R be the random variable counting the number of heads in each outcome. For example, if the outcome is tth, then =Rtth1. Suppose that the random variable X is defined in terms of R as follows: =X−R2−3R4. The values of X are given in the table below. Outcome htt tht hth thh ttt hhh hht tth Value of X −6 −6 −6 −6 −4 −4 −6 −6 Calculate the values of the probability distribution function of X, i.e. the function p X. First, fill in the first row with the values of X. Then fill in the appropriate probabilities in the second row.
Benford's Law claims that numbers chosen from very large data files tend to have "1" as the first nonzero digit disproportionately often. In fact, research has shown that if you randomly draw a number from a very large data file, the probability of getting a number with "1" as the leading digit is about 0.301. Suppose you are an auditor for a very large corporation. The revenue report involves millions of numbers in a large computer file. Let us say you took a random sample of n = 250 numerical entries from the file and r = 60 of the entries had a first nonzero digit of 1. Let p represent the population proportion of all numbers in the corporate file that have a first nonzero digit of 1. Test the claim that p is less than 0.301 by using α = 0.01. What does the area of the sampling distribution corresponding to your P-value look like? a. The area in the right tail of the standard normal curve. b. The area not including the right tail of the standard normal curve.…

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