Mathematics: A Practical Odyssey
8th Edition
ISBN: 9781305104174
Author: David B. Johnson, Thomas A. Mowry
Publisher: Cengage Learning
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Chapter E, Problem 20E
To determine
The more crowded state by computing the number of square feet per person in each state.
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Solve the given symbolic initial value problem and sketch a graph of the solution.
y"+y=38 (1-2); y(0) = 0, y'(0) = 2
Solve the following system of equations:
50x+20y=1800
10x+3y=300
5. State space models
Consider the model
T₁ = Tt−1 + €t
S₁ = 0.8S-4+ Nt
Y₁ = T₁ + S₁ + V₂
where (+)
Y₁,..., Y.
~
WN(0,σ²), nt ~
WN(0,σ2), and (V)
~
WN(0,0). We observe data
a. Write the model in the standard (matrix) form of a linear Gaussian state space model.
b. Does lim+++∞ Var (St - St|n) exist? If so, what is its value?
c. Does lim∞
Var(T₁ — Ît\n) exist? If so, what is its value?
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Mathematics: A Practical Odyssey
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- do question 2 pleasearrow_forwardFind the first four nonzero terms in a power series expansion about x=0 for a general solution to the given differential equation w''-14x^2w'+w=0arrow_forwardLet X represent the full height of a certain species of tree. Assume that X has a normal probability distribution with mean 203.8 ft and standard deviation 43.8 ft. You intend to measure a random sample of n = 211trees. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis (each tick mark) is one standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places. Image attached. I filled in the yellow boxes and am not sure why they are wrong. There are 3 yellow boxes filled in with values 206.82; 209.84; 212.86.arrow_forward
- Answer this questionarrow_forwardIn this exercise, we will investigate a technique to prove that a language is notregular. This tool is called the pumping lemma.The pumping lemma says that if M = (S, I, f, s0, F ) is a DFA with p states (i.e., p = |S|) and if the wordw is in L(M ) (the language generated by M ) and w has length greater than or equal to p, then w may bedivided into three pieces, w = xyz, satisfying the following conditions:1. For each i ∈ N, xy^i z ∈ L(M ).2. |y| > 0 (i.e., y contains at least one character).3. |xy| ≤ p (i.e., the string xy has at most p characters). Use the pumping lemma to show the following language is not regular (HINT: Use proof by contradictionto assume the language is regular and apply the pumping lemma to the language):L = {0^k1^k | k ∈ N}arrow_forwardA prefix of length ℓ of some word w are the first ℓ characters (in order) of w.1. Construct a context-free grammar for the language: L = {w ∈ {a, b}∗ | every prefix of w has at least as many a’s as b’s}2. Explain why every word generated by your context-free grammar (in Part 1) is contained in L. Then,prove via induction that every w ∈ L is produced by your context-free grammar.arrow_forward
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