A manuscript is sent to a typing firm consisting of typists A,B, and C. If it is typed by A, thenthe number of errors made is a Poisson random variable with mean 2.6; if typed by B, then thenumber of errors is a Poisson random variable with mean 3; and if typed by C, then it is aPoisson random variable with mean 3.4. Let X denote the number of errors in the typedmanuscript. Assume that each typist is equally likely to do the work. Find E (X) andVar (X).

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Answered: A manuscript is sent to a typing firm…

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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Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and σ = 0.70 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is μ = 4.45 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.45 grams? Use α = 0.05. How to solve for p
COVID-19 vaccination is important to help stop the COVID-19 pandemic. A survey conducted showed that only 15% of the Dehli community disagree with the COVID-19 vaccination program. Twenty people of the Dehli community were randomly selected.Let Y be the number of people who disagree with the newly COVID-19 vaccination program among the selected Sirdang community. a. state the distribution of Y and give its probability distribution function b. what is the probability that all of them agree with the vaccination program? c. calculate the probability of Y not exceeding its mean.
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.
Please answer q's a, b, and c For this case, a=3, b=9, and label the random variable A. Student ID number: 300546514
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and ? = 0.86 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is ? = 4.60 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.60 grams? Use ? = 0.10. (a) Compute the z value of the sample test statistic. (Round your answer to two decimal places.) (b) Find (or estimate) the P-value. (Round your answer to four decimal places.)
If a variable can take certain integer values between two given points, then it is called O a. Continuous random variable O b. Probabilistic random variable c. O c. Deterministic random variable O d. Uncertain random variable O e. Discrete random variable
The number of students who fail per semester is often modeled as a Poisson random variable. Assume that on the average there are 5 students who fail per sem. a. What is the probability that there are exactly 5 students who fail in 1 sem? b. What is the probability that there are exactly 2 students in one academic year? c. What is the probability that there are at least 2 students who fail in one sem?
A certain gene controls plant height. There are two alleles: B, the dominant allele, which produces tall plants, and b, the recessive allele, which produces short plants.Two heterozygous plants cross, producing 100 offspring. Assume each offspring's genotype is independent, and that each parent's allele is equally likely. Let S denote the discrete random variable which counts the number of short offspring. a. What is the probability that a randomly chosen offspring is short? b. What type of distribution does S have? What are the parameters of this distribution? c. What is the expected number of short offspring? d. What is the probability that among all 100 offspring, between 10 and 30 (both inclusive) are short? NEED HELP WITH A-D
3. An integer is randomly chosen from the set 1, 2,..., 100. If this integer is divisible by 2 we let Y = 0, and if it is not divisible by 2 but is divisible by 3 then Y = 1. We let Y = 2 in all other cases. Find mean and variance of Y.
prove that if random variables X and Y have same characteristic function, then have same distribution.
A robot is going to attempt the same task 100 times. Each time it tries, it will either succeed or fail to succeed in completing the task. Say the robot does not learn from its tries, so each attempt at the task is independent of the others. On a given attempt, the probability of the robot succeeding is 0.85. Let X be the random variable of the number of times this robot is able to succeed in completing the task. a. Find another way to compute the needed probability. b. Now say two robots are going to attempt the same task. The robots operate independently from one another. What is the probability that both robots succeed less than or equal to 80 times out of 100? c. Continuing with the situation in part e. with two independent robots. What is the probability that exactly one of them succeeds less than or equal to 80 times out of 100 ?
Bill Alther is a zoologist who studies Anna's hummingbird (Calypte anna).† Suppose that in a remote part of the Grand Canyon, a random sample of six of these birds was caught, weighed, and released. The weights (in grams) were as follows. 3.7 2.9 3.8 4.2 4.8 3.1 The sample mean is x = 3.75 grams. Let x be a random variable representing weights of hummingbirds in this part of the Grand Canyon. We assume that x has a normal distribution and o= 0.88 gram. Suppose it is known that for the population of all Anna's hummingbirds, the mean weight is = 4.65 grams. Do the data indicate that the mean weight of these birds in this part of the Grand Canyon is less than 4.65 grams? Use x=0.10. (a) What is the level of significance? State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? OH μ 4.65 g; right-tailed OH = 4.65 g; H₂ μ< 4.65 g; left-tailed OH = 4.65 g; Hμ 4.65 g; two-tailed (b) What sampling distribution will you use? Explain the rationale…

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