Consider two independent Bernoulli processes X1[n] and X2[n] both have success probability 0.50. They are merged into one Bernoulli process andthen later split into Y|[n] and Ya[n] with equal success probabilities. What is the probability that Y1[71] = 0 given that Ya{n] = 07 Specifyoanswer correct up to four decimal places.Answer:

Answered: Consider two Independent Bernoulli…

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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On each trial of an experiment, a subject is presented with a constant soft noise, which is interrupted at some unpredictable time by a noticeably louder sound. The time it takes for the subject to react to this louder sound is recorded. The following list contains the reaction times (in milliseconds) for the 16 trials of this experiment: 285, 175, 164, 217, 273, 222, 212, 202, 236, 229, 171, 235, 193, 186, 261, 241 Send data to calculator th Find 40" and 75" percentiles for these reaction times. (a) The 40 th percentile: || milliseconds (Ь) The 75 th percentile: milliseconds
At any age, about 20% of American adults participate in physical conditioning activities at least twice a week. However, these activities change as people get older, and occasionally participants cease to be older as they age. In a local survey of n = 100 adults over 40 years of age, a total of 15 people indicated that they participated in these activities at least twice a week. Does this data indicate that the percentage of participation for adults over 40 years of age is considerably less than the 20% figure? Find the p-value and use it to draw the appropriate conclusions.
A research center claims that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At α=0.10, is there enough evidence to reject the research center's claim? 1. Let p be the population proportion of successes, where a success is an adult in the country who wouuld travel into space on a commercial flight if they could afford it. State the H0 and the Ha. 2. Identify the standardized statistic and round 2 decimals if needed. 3. Identify the p value. 4. Decide whether to reject or fail to reject the null hypothesis adn interpret the decision in the context of the original claim. (Reject or fail to reject) the null hypothesis. There (is or is not) enough evidence to (reject or support) the researcher's claim.
Let {e} be a zero-mean, unit-variance white noise process. Consider a process {Y} which starts at time t = 0, and is defined recursively as follows: Let Yo = cieo, Y₁ = c₂Yo + e₁, and Y₁ = ¢₁Yt-1 + 2Yt-2 + et for t≥ 2 (as in an AR(2) process). a) Show that the process has zero mean. 1 b) For values of 01, 02 in the stationarity region for an AR (2) process, show how to choose C₁, C₂ such that both Var(Y) = Var(Y₁) and the lag 1 autocorrelation cov(Yo, Y₁) equals that of a stationary AR(2) process with parameters 01, 02. c) Once the process {Y} has been generated, show how one can transform in into a new process which has any desired mean and variance. (Remark. This gives a method for simu- lating stationary AR(2) processes.)
A medical researcher says that less than 86% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 300 adults in that country, 84% think that healthy children should be required to be vaccinated. At α=0.05, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. Less than 8686% of adults in the country think that healthy children should be required to be vaccinated. B. The percentage of adults in the country who think that healthy children should be required to be vaccinated is not nothing%. C. nothing% of adults in the country think that healthy children should be required to be vaccinated. D. More than nothing%…
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.…
A sleep researcher is interested in learning about how to help people fall asleep faster at night without taking medicine. She asks n = 13 individuals to wear a device to bed for two weeks straight. Half of the participants were asked to spray their pillows with a lavender mist for the first week then sleep with a regular "unscented" pillow for the second week. The other half of the participants were asked to do the same thing, but in the opposite order: unscented pillow then lavender misted pillow. Testing at an alpha level of a = .01, she expects the lavender scented pillow to decrease the amount of time it takes people to fall asleep. State the Hypotheses 2 3 4 5 Ho: Subject 6 7 H₁: 8 9 10 11 12 13 MD= = Determine the critical region and draw it on the distribution above: Calculate the test statistic using the following sample data below: 360 sec 420 sec 480 sec tcritical = Regular Lavender Pillow Pillow 420 sec 420 sec 480 sec 480 sec 360 sec 360 sec 420 sec 420 sec 420 sec 420 sec…

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