2. 1 3 Let A = |0 2 -1 Lo 2. a) Show that (A – 21)³ = 0 . Calculate e4-21 b) Use the fact that A(21) = (21)A to compute e4

Q: 12. Define def M e-$dWg• s=0 For each t > 0, compute (a) E[M¡]. (b) E[M?]

A: Given  Mt=∫s=0te-s dWs      , where W is a Brownian motion.

Q: 2. Let {N(t),t 2 0} be a renewal process and (X,,X,, X,.-be the corresponding interarrival times.…

A: A renewal process is a stochastic model that occurs at random and is temporal based. The process…

Q: Simplify the expressions in Exercises 65–68.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 9.8 Refer to Exercise 9.6. You want to test Ho : µ = 2.3 against H : µ > 2.3. Find the critical…

A: given  information  hypothesis H0 : μ =2.3 H1 : μ >2.3 the sample size is n =35 mean is 2.4…

Q: A. let w-e te Find W2

A: We can solve this using u/v rule

Q: 23 4- [fe** dycdx ans :(e' - e' )(e² – e') 12

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Q: 1. Prove That E (ri + si) a; = E}-1ri a; + £?=1 Sį a¿ 2. Find E(-1)k+1 (2k) k=1 3. Given X = 2, 4,…

A: 1)  LHS=∑i=1n ri+si ai          = r1+s1 a1+ r2+s2 a2 + ..................+ rn+sn an          =…

Q: Can you please answer this question?

A: (a)

Q: 62 0 <I <1 Q3 Compute E (X) given that fx (x) otherwise

A: The formula of E(X) is,

Q: 10 9.3 10.1 (X/x) = l10.1 [37.7] Y = 52.5 23.4] 9.3 12 6 RSS= 6.2 17.1 1. Estimate B В2 Вз 2. Test…

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Q: 3. Suppose the population of Winneba is approximated by P(t) = P,e03, where t is measured in years…

A:

Q: 3. A machine has n components, the lifetimes of which are independent. However the whole machine…

A: Since you have asked multiple question, according to our guidelines we will solve the first question…

Q: Example 7.13. Apply Bessel's formula to obtain y25 given y20 2854, y24 = 3162, y 28 = 3544, y 32 =…

A: Here we need to use bessel's formula to solve this problem.

Q: 8. Given that (2x-x*); 0<x<2, S(x) = ; elsewhere. a) Calculate E(X), E(X²) and E 2- X

A:

Q: 7:37 PM Thu Feb 10 2-3-3 Learning R HC RD 4 COH - 65 mRD =

A: Given:

Q: Find the first term of: E (-1)n+1 (z+1)" n=1 3D1 O (z+1)^2]/2 Z+1 -(z+1) no solution

A:

Q: inspecting devices to sample a fraction of their output for quality control purposes. The first…

A:

Q: Let X =1 if a randomly selected vehicle passes an emissions test and X = 0 otherwise. Then X is a…

A: Given that X=1 if a randomly selected vehicle passes an emission test and X=0 otherwise and X is a…

Q: e a. y; = +e-2= In(e" +1) +e-* In(e" + 1) – 6 2 b. Y, = re2" + e In(1 + e") – e2" In(1+ e") C. Y; =…

A: Option (a) is correct.   See the solution in the attachment.

Q: e -1 Compute Lt v1+x-1

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Q: According to a report from the United States Environmental Protection Agency, burning one gallon of…

A: Test hypotheses: The hypotheses are given below: Null hypothesis: H0 : μ = 8.9 That is, the…

Q: Exercise 7.9 The model is Y = Xß + e with E (e | X] = 0 and X € R. Consider the two estimators (b)…

A:

Q: Let a be a constant. Given that 3x In(ax)dr = e18 ( 36 -89 , find In a. 3

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Q: - S e-ttat1-1 dt a # 1 a '0

A: We use the definition of the Gamma Function to solve the given question.

Q: 84. a. Prove that e > 1 + x if x > 0. b. Use the result in part (a) to show that e 21+x + r.

A: Answer (a): To prove : ex≥1+x if x≥0 The given inequality can also be written as: ex≥1+xex-1-x≥0

Q: 25. The populations, P, of six towns with time t in years are given by (i) P = 1000(1.08)t (ii) P…

A:

Q: 19. Quotations of Index Numbers of security prices of a certain joint stock tompany are given below…

A:

Q: Determine the general solution of the following Bernoulli ODE: y' + xy = x³y³

A:

Q: alpha iõtä 100 rhô 2 beta 20 kappa 200 sigma K 3 gamma 30 lambda 300 tau 4 delta 40 mu 400 upsilon 5…

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Q: Show by example that E=1a,b, may diverge even if E=1an and E=1b, both converge.

A: According to the ratio test, determine the value of limit. If L&lt;1, the series is convergent. If…

Q: 10) Let A E Mnxn be given by 0 0 ao ... -1 .. A = -1 0 a2 .. 0 0 0 • -1 an-1 .. Compute XA(t).

A:

Q: 4. Find C1, C2, and C3 so that the given functions will satisfy the prescribed initial conditions.…

A: y(x) = c1ex+c2e2x+3ex  y(0) =y'(0) = 0  We have to find c1 and c2 . Note: According to Bartley…

Q: 17. Let a, = (-1)" vn 2 1. Calculate the value of an+1 - a, for odd values of n. A.-1 В. -2 С. 2 D.…

A: Given sequence is  an=(-1)^n

Q: In 5 e'dt 2t e 0 V e 2t + 64

A:

Q: 4. Exercise §3.4 #47. Let n €Z with n> 0. Prove that E - a(n)

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Q: Calculate the residue of e.e5=0

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Q: 3 (5) Suppose that T : R³ → R² „such that 2 1 1 T (e,) = T(e.) T(e,) = and T (e,) = 1 1 3 2 T Find -…

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Q: c). Invest diFrgate whether the given en equation is homogene eous dy 2. oxy

A: A first order differential equation is homogeneous when it can be written as a function of y/x, that…

Q: 12 7 3 22 or 1 5 x, - 7 -11 || x; 7 and using [ x x3]=[1 2 1]. as t lues of X x x at the end of the…

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Q: Example 19-36. If U, = a + bx+cx², prove that 3 U, dx = 2U2 + 12 (Uo- 2U2 + U4) 1 and hence find an…

A:

Q: Show that S ťe dt = 3VI

A:

Q: If z3 + In(e 2 -2 e+e) = 0 az find at the point (0,0) O -3 0 3 О-2 O 2

A:

Q: Theorem 17-2. Let {T„} be a sequence of estimators such that for all 0 e 0, and (ii) Vare (Tµ) →0,…

A:

Q: Let c, = M and Cn = 2cn-1 - 1 for Vn eZ+ - {1}, find the explicit formula for the nth term for n…

A:

Q: 13+ 7+1 The long-run behavior of r(t) is 1+-t

A: Long run behavior of given function can be calculated using leading terms of numerator and…

Q: _11.x = 80 C. 0.43 D. -0.43 A. 1.30 B. 0.96 12. x = 70 C. 0.43 D. -0.43 A. 1.30 B. 0.96 _13.x= 90 C.…

A:

Q: Find the radius of convergence and interval of convergence of  Σ 1 to infinity…

A:

Q: Theorem 17-6. If T, is an MVUE of y(0) and T2 is any other unbiased estimator of y(9) with…

A:

Q: 5. Let M = [-24 3]. Determine a constant C such that (CM)( CM") = [261]. Is there more than one…

A: Given M=-2 4 3

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.