Consider two independent Bernoulli processes X₁ [n] and X₂ [n] both have success probability 0.50. They are mergedinto one Bernoulli process and then later split into Y₁ [n] and Y₂[n] with equal success probabilities. What is theprobability that Y₁ [n] = 0 given that Y₂ [n] = 0? Specify your answer correct up to four decimal places.

Given: The two independent Bernoulli processes X1n and X2n both have success probability 0.50. They…

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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The nAChR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (O) with transition probabilities (per one microsecond): 0.04 (from R to C), 0.07 (from C to R), 0.12 (from C to O) and 0.02 (from O to C); the other transition probabilities are 0. Calculate the probability of the following string of states: OCCR, taking the first state as given. (Enter three digits after the decimal).
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.
Pedestrians approach a crossing from the left and right sides following independent Poisson processes withaverage arrival rates of λL = 5 and λR = 1 arrivals per minute. Each pedestrian then waits until a lightis flashed, at which time all waiting pedestrians must cross to the opposite side (either from left to right orfrom right to left). Assume that the left and right arrival processes are independent, that the light flashesevery T = 2 minutes, and that crossing takes zero time – it is instantaneous.1. What is the probability that in a particular crossing, there are total 10 pedestrian and they are allcrossing from left to right?
Could you solve (i), (ii), (iii)? Thank you.
An ion channel can be in either open (O) or closed (C) states. If it is open, then it has probability 0.1 of closing in 1 microsecond; if closed, it has probability 0.3 of opening in 1 microsecond.
A researcher is investigating the effectiveness of a new treatment for improving short-term memory. A sample of n = 8 participants is obtained. Each individual completes a short-term memory test and then begins a 4-week program of the new treatment. At the end of the program, the short-term memory is tested again and the researcher records the amount of difference between the two ratings. For this sample, memory scores increased by an average of M = 3.5 points with SS = 56. Can you conclude that the new treatment significantly improves (increases) short-term memory performance? Test with α = .05, one-tailed. a. state the null and alternative hypotheses b. Locate the boundary of the critical region c. Calculate the test statistic. t = ? d. what is the correct decision? e. Compute r2 to measure the size of the treatment effect. (Round to three decimal places)
If λ = 6 per hour and μ = 6 per hour in an (M/M/1): (5/FIFO) model, find the probability that there is no customer in the system.
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 fallowing list contains the reaction times (in milliseconds) for the 16 trials of this experiment: 241, 271. 261, 164, 257, 193. 186, 222, 226, 212, 152, 273, 217, 171, 175, 202 Send date to caleulator Find 40 and 75" percentiles for these reaction times. (a) The 40 percentile: Imilliseconds (b) The 75t percentile: miliseconds
Define the random process {Xt} by Xt = et + θ et−1. Show this process is weakly stationary.
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…
Exercise 2. A r.v. X is Poisson distributed with parameter λ = 5.5. (a) Calculate the probability that X = 3. (b) Calculate the probability that X < 2. (c) What is the most likely (i.e. highest probability) value for X ? (You can make a graph of f(x) to find the answer).

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