The nACHR ion channel can be in one of three states: resting (R), closed with Ach bound (C), and open (O) with transitionprobabilities (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); theother transition probabilities are 0. Calculate the probability of the following string of states: OCCR, taking the first state asgiven. (Enter three digits after the decimal). Report the probability of the Resting state in the stationary distribution for the three-state nAchRion channel model to two digits after the decimal.

From the given transitions probabilities for the respective states of R, C, and O, it is obtained…

Answered: The nACHR ion channel can be in one of…

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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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).
The observation on the time series variable Y made at date t is denoted as Y, and the total number of observations is denoted as T. Suppose Y represents GDP of a country. A researcher has the past 10 years of GDP data, from 2009 to 2019. Yj is the GDP for the year t-j (j=t,., T, and t=0, 1, 2,.., 10) and Y; is the GDP for the current year. The researcher wants to estimate the first four autocorrelations, p, =1,.., 4), using this data. Suppose Var(Y,) = 19.16. Also assume that the first four autocovariance estimates are as follows: j=1 j=2 j=3 j=4 15.98 13.69 12.76 11.14
A pseudo-random signal (S) of -3 or 3 is transmitted over a noisy channel. S=-3 is transmitted with probability of 1/3. The received signal, Y, is the sum of the sent signal and the noise, N. The noise is modeled as a normal Gaussian with E[N]=0,var(N)=4 . The received signal is decoded as -3 for Y≤−0.5 and 3 for Y>−0.5. a. What is the probability of error in this system? b. To improve the system, each signal is transmitted three times and output is determine by majority rule (2 or more). What is the new probability of error?
You work for an insurance company and are studying the relationship between types of crashes and the vehicles involved. As part of your study, you randomly select 3589 vehicle crashes and organize the resulting data as shown in the contigency table. At α=0.10, can you conclude that the type of crash depends on the type of vehicle? Complete parts (a) through (d). Vehicle Type of crash Car Pickup Sport utility Single-vehicle 866 323 340 Multiple-vehicle 1145 487 428 Question content area bottom Part 1 (a) Identify the claim and state the null and alternative hypotheses. H0: The type of crash and the type of vehicle are ▼ independent dependent . Ha: The type of crash and the type of vehicle are ▼ dependent independent . The ▼ alternative hypothesis null hypothesis is the claim.
Ramp metering is a traffic engineering idea that requires cars entering a freeway to stop for a certain period of time before joining the traffic flow. The theory is that ramp metering controls the number of cars on the freeway and the number of cars accessing the freeway, resulting in a freer flow of cars, which ultimately results in faster travel times. To test whether ramp metering is effective in reducing travel times, engineers conducted an experiment in which a section of freeway had ramp meters installed on the on-ramps. The response variable for the study was speed of the vehicles. A random sample of 15 cars on the highway for a Monday at 6 p.m. with the ramp meters on and a second random sample of 15 cars on a different Monday at 6 pm with the meters off resulted in the following speeds (in miles per hour). (a) Uraw side-by-side Doxplots of each data set Does there appear to be a merence in the speeds? Are there any outlers? Choose the correct Dox plot below. A. 0 Off 15 30 45…
Consider two securities, the first having μ1 = 1 and σ1 = 0.1, and the secondhaving μ2 = 0.8 and σ2 = 0.12. Suppose that they are negatively correlated,with ρ = −0.8. Denote the expected return and its standard deviation as functions of π byμ(π ) and σ (π ). The pair (μ(π ), σ (π )) trace out a curve in the plane as πvaries from 0 to 1. Plot this curve in R.
Let X; be random variables and M; (t) be their respective moment generating functions, for i = 1, 2, 3. Solve: Suppose that M₁ (t) = 1 +t+t² + t³+... Is this enough information to determine the type of random variable that X₁ is? Explain why or why not. Determine the type of random variable if there is enough information. Determine if it is possible for M₂ (t) = (-1)" -0 (2n)! possible, determine the type of random variable that X₂. -+2n. Explain why or why not. If it is Suppose that that the expectation of X3 is -1 and its second moment is 1. Determine if this is enough information to find the moment generating function of X3 explicitly. Explain why or why not. If it is enough information, compute it explicitly.
For random variables X and Y such that E(X) = 2, E(Y) = 1, E(X²) = 10, E(Y²) = 3, and E (XY) = c, Find: а. Var(3X — 5Y). b. The correlation coefficient between X and Y, p. The range of values of c for which the assumptions of the problem are consistent. С.

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