In the first hour of customers using the app they served 180 customers. STACOdecided to treat this hour as 60 non-overlapping intervals of one minute each.They then assumed they could model the number of customers served eachminute by independent and identically distributed Poisson Random Variables.They called the number of customers served in the ith minute X₁, soX₁ + X₂ + ... + X60180, X₁~ Poisson(X), and X; and X, are independentif i j.-STACO used this to compute an estimated 95% confidence interval and thentold Coffee Kart that they could claim to serve an average of three customersper minute.=i Recall that the maximum likelihood estimator of A is A X. Using thesame assumptions as STACO and assuming that n is large enough toapply the Central Limit Theorem, calculate an estimated 95% confidenceinterval for X.ii Do you agree with the assumptions made by STACO. Justify your answer.

In the first hour of customers using the app they served 180 customers. STACO decided to treat this…

Answered: In the first hour of customers using…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Three components are randomly sampled, one at a time, from a large lot. As each component is selected, it is tested. If it passes the test, a success (S) occurs; if it fails the test, a failure (F) occurs. Assume that 82.0% of the components in the lot will succeed in passing the test. Let X represent the number of successes among the three sampled components. Find P(X= 3). (Round the final answer to three decimal places.)
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.
In experiment of flipping two coins, each coin has two faces: Head and Tail. Each face is being equally likely to be drawn. If two random variables X and Y are defined as X(s) = Number of Heads appeared on both coins Y(s) = Number of Tails appeared on both coins The value of pxy (2,0) is 00.5 00 01 00.25
Let a be a random variable representing the percentage of protein content for early bloom alfalfa hay. The average percentage protein content of such early bloom alfalfa should be u = 17.2%. A farmer's co-op is thinking of buying a large amount of baled hay but suspects that the hay is from a later summer cutting with lower protein content. A small amount of hay was removed from each bale of a random sample of 50 bales. The average protein content from the samples was determined by a local agricultural college to be -15.8% with a sample standard deviation of S = 5.3%- At a = .05, does this hay have lower average protein content than the early bloom alfalfa?
Complete the following multiple choice questions. No work will be graded in the bonus problem. (a) E(X²)= 16. Compute E[-X(3X – 2)]. Assume that X is a random variable with E(X)= -3 and | (i) -54 (ii) -48 (iii) -33 (iv) -27
A manager of a product sales group believes the number of sales made by an employee (Y) depends on how many years that employee has been with the company (X1) and how he/she scored on a business aptitude test (X2). A random sample of 8 employees provides the following (refer Table 4): Employees y X1 X2 1 100 9 6 2 90 4 10 3 80 8 9 4 70 5 4 5 60 5 8 6 50 7 5 7 40 2 4 8 30 2 2 (a) Run a regression analysis based on the data in Table 4 using Mic. Office EXCEL. Based on theoutput, propose a regression equation that can be used to predict paralegal GPA.(b) Interpret the coefficient value of each independent variable in the constructedmodel(c) Is each independent variable sharing a significant linear relationship with the dependent variable?Verify at 0.05 level of significance. Make your conclusion based on the p-value in the EXCEL output.
Three batteries with a life span of 1 day were used simultaneously for one day. Battery usage follows a uniform distribution and three batteries are used independently of each other. Find the PDF of the sum of the remaining three batteries after the day.
Suppose that X is a N(3,4) random variable and suppose that Y=5X+2. Determine P(Y>18.5).
Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.f. Why are the estimated waits in this system so long? Are the assumptions behindthem reasonable? Why or why not?
On each trial of an experiment, a participant is presented with a constant soft noise, which is interrupted at some unpredictable time by a slightly louder sound. The time it takes for the participant to react to the louder sound is recorded. The following list contains the reaction times (in milliseconds) for 26 trials of this experiment. 156, 202, 214, 222, 234, 250, 279, 280, 280, 297, 298, 299, 301, 303, 311, 329, 340, 358, 373, 394, 419, 436, 451, 583, 701, 864 Send data to Excel Aa Frequency 12 12- 10 10- 8- 6. 4. 2 2- 150 300 450 600 750 1000 Reaction time (in milliseconds)
A fair dice is thrown once. The random variable Y is related to the number B thrown on the dice as follows. If B is even, then Y is half B, otherwise Y is triple B. Find the mode and E(Y). Select one: no mode and E(Y) = - mode = 3 and E(Y) = 4 mode = 2 and E(Y) = mode = 3 and E(Y) = mode = 5 and E(Y) =

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