Consider the following OCV-SOC model: V0(s) = k0 + k1s + k2s 1 + k3s 2 + k4s 3 + k5s 4 + k6 ln(s) + k7 ln(1 s) (1) where k0 = 9.082, k1 = 76.604, k2 = 103.087, k3 = 18.185, k4 = 2.062, k5 = 0.102, k6 = 141.199, and k7 = 1.117. These parameters were computed for SOC values s [0, 1] after they were linearly scaled to s 0 [.175, .825].

find the SOC of the given battery corresponding to a measure OCV of 3.75 V. Assume that there is voltage measurement error and we need to find out the resulting SOC error. It is given that the voltage measurement error is zero-mean with standard deviation 10 mV.

(a) Use the following Monte-Carlo simulation approach to find out the standard deviation of the error in SOC error

- Generate 1000 'voltage measurements' using the above-mentioned measurement error (zero-mean, standard deviation of 10 mV). The Matlab command '3.75 + 0.01*randn(1000,1)' will generate these 1000 measurements. The standard deviation of these measurements is 0.01 V (or 10 mV). - Compute the SOC corresponding to each of these 1000 voltage measurements

- Compute the SOC corresponding to OCV = 3.75 V

- Compute the SOC computation error corresponding to each of the 1000 measurements

- Compute the standard deviation of the SOC computation error

(b) Repeat the above for SOC estimation corresponding to an OCV of 3.95 V

(c) Repeat the above for SOC estimation corresponding to an OCV of 3.6 V

(d) Repeat the above for SOC estimation corresponding to an OCV of 3.3 V

(e) Consider the following statement: "Given the same voltage measurement, the error in computed SOC varies depending on the SOC region" Do you agree or disagree with the above statement? justify your answer.

Problem 1: A Central Limit Theorem Simulation Here we will perform a Central Limit Theorem simulation similar to the ones done in class. That is: . Pick a distribution (that was not presented in class) . Justify that the distribution will abide by the central limit theorem . Find a parameter set and value for / where we can see that the central limit theorem clearly applies . Find a parameter set and value for / where we can see that the central limit theorem does not apply . Code must be submitted (preferably in R, but MATLAB, Python, ForTran, and C++ will also be accepted).(OLS formula for bivariate case) Let our model be the bivariate specifcation we learned before, that is, y = a + x + u. Use the OLS formula in matrix form to confirm the estimators a^ and B^ for the bivariate case (OLS formula for bivariate case) Let our model be the bivariate specification we learned before, that is, y = a + Br + u. Use the OLS formula in matrix form to confirm the estimators a and 8 for the bivariate case.Consider a three-state continuous-time Markov chain in which the transition rates are given by 0 Q A 0 0 A O The states are labelled 1, 2 and 3. (c) Use the results of Problem 1 to solve the backward equations of this 3-state Markov chain.Question 21 4 If you don't know whether the frequency distribution is normally distributed. O You can use both the Empirical Rule and the Central Limit Theorem O You can't use the Empirical Rule, but you can use the Central Limit Theorem O You can't use the Central Limit Theorem, but you can use the Empirical Rule You can't use either the Empirical Rule or the Central Limit Theorem