2)A Marhor chain Zxn3nzo has 3 dates : a1,2. It's tronsition mobalility matrix : io P = ,2 .6.2 0.6.4, and imtial distribution PCXO-0)-.3 PCX, =D=3 4.3.3 Find P(X3-1|X-0) PCKo=2)=14
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- 2. Suppose that in Example 2.27, 400 units of food A, 500 units of B, and 600 units of C are placed in the test tube each day and the data on daily food consumption by the bacteria (in units per day) are as shown in Table 2.7. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.7 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 3 Food C 1 1 1A 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?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?
- Then, what does the equation, d/dt Π = MΠ means? (where M is a 4x4 transition rate matrix)Consider the linear model Yi = B0 + B1X1i + B2X2i + ui where ui is the error term and where E(ui|X1i,X2i) = 0, observations (Yi,X1i,X2i) are independent and identically distributed, 0 < E(Y4) < 1, 0 < 1i E(X14i) < 1, 0 < E(X24i) < 1 and where X2i = X12i. Are the OLS estimators Bˆ1 and Bˆ2 of the coe¢cients B1 and B2 unbiased and consistent? Explain.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.
- 4) Here are data on the lengths of male and female roaches (in mm). Your job is to find out if there is adifference between male and female roaches (this should be two sided - why?).males 15.4 13.9 12.7 9.6 6.6 10.7 9.9 13.3 16.2 9.0 11.4 16.6 12.2females 16.7 16.3 12.8 16.9 15.1 12.8 18.7 18.3 8.6 13.6 15.3 16.2 13.4It's up to you to figure out what the best procedure is, what kind of hypotheses to use, which α to use,what test to use, and so on. Make sure you follow all the appropriate steps. You should probably use Ras you’ll get done much quicker. Remember to very clearly state your results in writing. Never turn in just an R printout .Hint: how do you decide which test to use? What kind of distributions do the data have?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 40% of people who were low users one month will be low users the next month and that 30% 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. After many months, how many % of the customers are high users5) If B arises from a matrix A by elementary row operations, what is the relationship between NS(A) and NS(B)?
- Show what correction (using the generalized least squares method) we should use if the form of heteroskedasticity was the following, show mathematically For both a) and b)Consider one application in which either a first order or second order IVP is formed to find a solution in a model problem.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)