Specifically, you are required to generate and plot 2-dimensional Gaussian random vector with z mean vector and the covariance matrix given by 1 p k for k = 1,2,.,9. 10 where p=
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- In an office complex of 1110 employees, on any given day some are at work and the rest are absent. It is known that if an employee is at work today, there is an 77% chance that she will be at work tomorrow, and if the employee is absent today, there is a 54% chance that she will be absent tomorrow. Suppose that today there are 854 emplovees at work. Find the steady-state vector. (Note that the sum of the entries must be the total number of employees, but make sure that your answers are correct to at least 1 decimal place.)1) Assuming you have a data matrix X that has n rows and p variables and you know both µ and Σ. How is (X- µ)‘Σ-1(X- µ) distributed? 2) Assuming that you don’t know the values of µ and Σ. How is the statistical distance distributed as n-p gets large?1- The number of items produced in a factory during a week is known to be a randomvariable with mean 50● Using Markov's inequality, what can you say about the probability that this week'sproduction exceeds 75?● If the variance of one week's production is equal to 25, then using Chebyshev'sinequality, what can be said about the probability that this week's production isbetween 40 and 60?
- If the probability vector is [0.6 0.4 ] and the transition matrix is (0.5 0.5) (0.9 0.1), find the resulting 18th probability vector.Suppose that {Xn} is a Markov chain with state space S = {1, 2}, transition matrix （1/5 4/5 2/5 3/5）, and initial distribution P (X0 = 1) = 3/4 and P (X0 = 2) = 1/4. Compute the following: P(X2 =2)A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?
- Show that if X is not a deterministic random variable, then H(X) is strictly positive. What happens to the probabilities if a random variable is non-deterministic?In the Heidman’s Department Store problem of Unit 2 of this module, suppose that the following transition matrix is appropriate:If Heidman’s has $4000 in the 0–30-day category and $5000 in the 31–90-day category what is your estimate of the amount of bad debts the company will experience?Consider a dynamic system with three states, s_1s1, s_2s2, and s_3s3. Let A = \begin{pmatrix} 0.7&0.3 &0.3 \\0.2& 0.6 & 0.2 \\ 0.1 & 0.1 &0.5 \end{pmatrix}A=⎝⎛0.70.20.10.30.60.10.30.20.5⎠⎞ be the transition matrix such that a_{ij}aij is the probability of moving from s_jsj to s_isi. Let \overrightarrow{x} = \begin{pmatrix}x_1\\x_2\\x_3\end{pmatrix}x=⎝⎛x1x2x3⎠⎞ be a stationery distribution of AA with sum of elements x_1+x_2+x_3=120x1+x2+x3=120. Find x_2x2.
- if only given a column vector function (2x1), f(B) = [e^(B1) - 1 ; e^(B2) - 1], then how do you find the asymptotic variance-covariance matrix estimator using the Delta method?why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian MotionLet P be a 2 × 2 stochastic matrix. Prove that there exists a 2 × 1 state matrix X with nonnegative entries such that PX = X.