(a) Explain in words what the fact that p32 = 0 means about this disease.(b) The model is changed by giving p14 and P34 small positive values (and reducingP11 and p33 to keep the row sums equal to 1). What new feature does thismodel include?(c) The model is changed by giving p13 a positive value (and reducing p₁ to keepthe row sum equal to 1). What new feature does this model include?(d) The model is changed by giving p32 a positive value which is less that 0.01(and reducing P33 to keep the row sum equal to 1). What new feature does thismodel include?(e) Interpret the Markov property and the fact that p2,3 = 0.1 in words. 1. During a pandemic, a person's state of health is monitored by recording each daywhether they are• Healthy and have never been infected by the disease (state 1)• Infected with the disease (state 2)• Recovered from a previous infection of the disease (state 3)• Dead (state 4)Suppose that X is the state of health of a particular person on day t of the pandemicand that (Xo, X₁,...) is a Markov chain with transition matrix:0.99 0.01 0 000.899 0.10.00100100001

The provided transition matrix models the progression of a disease through a population, tracking…

Answered: (a) Explain in words what the fact that…

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 1EQ: 1. Suppose that, in Example 2.27, 400 units of food A, 600 units of B, and 600 units of C are placed...

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1. Suppose that, in Example 2.27, 400 units of food A, 600 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 2.6. How many bacteria of each strain can coexist in the test tube and consume all of the food? Table 2.6 Bacteria Strain I Bacteria Strain II Bacteria Strain III Food A 1 2 0 Food B 2 1 1 Food C 1 1 2
An ecologist is considering two different positions in which to setup his solar energy collector. He takes two identical collector places one in each of the positions and measure the energy in at collected as 10 consecutive days. Days 1 3 4 5 6 7 8 9 10 Position 2.6 5.4 3.2 5.0 4.3 2.7 2.6 3.9 6.0 1.6 POSITIO 2.8 5.1 3.1 6.0 4.6 3.2 2.9 4.5 6.2 2.2 Ny Test whether the difference of mean is significance ?
Can you give a scenario for e and f please?
Suppose that we have two independent data sets from the same process. One was collected in the past and another was collected recently. The observations are: {(r;; Yi), i = 1, n1} and {(r;, Yi), i = n1 + 1, .. , n1 + n2}. The two models are postulated to be 2. Yi ao + a1x; + Ei, i = 1, . . , n1, %3D = Bo + B1x; + Ei; i = n1 +1,,n, where n = nị + n2. a) Express these separate models as a single model in matrix form. b) Find A and c for testing Ho : a1 =
Let {X₁, X2,..., Xn} be the scores from Midterm 1 and {Y₁, Y2, ..., Ym} be those from Midterm 2. We assume that the scores in Midterm 1 are Normal (₁, 0) r.v.s and those of Midterm 2 are Normal(2, 02) r.v.s. In addition, scores are independent r.v.s within and between midterms. Our interest is to see whether there is a meaningful difference between the (population) averages, i.e., ₁-2. The most intuitive estimator for the quantity of interest is X-Y. Let us assume that of and o2 are completely known constants. Find a 95% confidence - interval for 1 2, using the exact method (pivotal quantity). (Hint: if X~ N(μ₁,02) and Y~ N(μ2, 02) and X and Y are independent, then X - Y ~ N(H₁-H₂,0² +03).)
4. Let (, F, P) be a probability space and let X and Y be random variables on it. Assume that the random variable X takes on value 0 and 1, and the distribution of X is given by Px (0)=0.3, Px(1) = 0.7. Further assume that the random variable Y takes on value 0 and 1, and the distribution of Y is given by Py (0)=0.8, Py(1) = 0.2. (i) Assume that the random variables X and Y are independent. Find the joint distribution of X and Y, Px,y. [5 Marks] (ii) Give an example of a possible joint distribution Px,y such that the random variables X, Y are not independent. [15 Marks] Hint. Denote Px,y (0, 0) = = a, Px,y (0, 1) = b, Px,y(1, 0) = = C, Px,y (1, 1) = = d. We must have (why?) a, b, c, d = [0, 1], a+b+c+d= 1, a+b= 0.3, a+c=0.8. Choose a, b, c, d satisfying the above conditions and such that a 0.24.
SECTION I0.4 Example 4: Let X, X2, ., X, be a random sample from N(0,0), find a C.S.S for 0. SEOTION IO.4 Example 5: Let X1, X2, . ,X, be a random sample from Beta(1,6), find a C.S.S for 0.
(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) or
Show that if a \b and gcd(b, c) = 1 Then gcd(a,c) = 1 %3D
6. Two independent random variables X1=(-1,0,1) and X2=(-1.0) can take the following probability values: P(X1-1)-p, P(X1=0)=2p, P(X1=1)=1-3p, P(X2=-1)=p, P(X2=0)=1-p. Si X=X1+X2 y Y=X1*X2, determine E(XY).
What does the memoryless property refer to? An event cannot occur if it has already occured within a recent specified time period. The distribution of the time until an event does not depend on how much time has already passed. The occurrence of an event is independent of the number of times that event has already occurred. None of the above. Suppose X~ GAM (a, 3). Which of the following statements are true? Select all that apply. 3 is a location parameter. E[X]=a3 a is a location parameter. 3 is a shape parameter. 3 is a scale parameter. a is a shape parameter. a is a scale parameter. For a > 1, the probability density function (pdf) is monotonic decreasing. For a < 1, the probability density function (pdf) is monotonic decreasing. None of the above.
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