5. Let X₁, X2,..., Xn be iid N(A, A²), A > 0. For this model both X and cS are unbiased √n - II ((n − 1)/2) - estimators of X, where c = √21(n/2) a. Prove that for any number b the estimator bX+(1-b) (cS) is an unbiased estimator of X. b. Find the value of b that produces the estimator with minimum variance in part(a). c. Show that (X, S²) is a sufficient statistics for X.

Q: Which of the following u-substitution should be used in evaluating {(2³_x)[x(x³_2x)]³} dz?

A: Given integration ∫{ ( x3 - x )[ x( x3 - 2x )]3} dx

Q: A 3. Find (f g)(x) if f(x) = x2+x +1 and g(x) = x2 - x- 1. %3D %3D O (f 9)(x) = a4+ 2a + 3x? +2x +1…

A: We can find (f·g)(x) as below

Q: 5. For the signal below find the following manipulations in time x(1) 12 а. [x (2t - 3)] b. x(1 –…

A: The solution is given below in the next step:

Q: The domain off(x) = 3-x is 1-x2 %3D 1. R 2. R/{1,-1} 3. R/{3} 4. (0, ∞)

A: Domain: The domain of a function is the set of all input values for which the function is defined.…

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A: Given information: Consider the given dataset: Actual Production Rate Simulation Result 432 444…

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A: Given that         f(x) = (1/2)√(x-2) + 8  Here we have to compute f-1(5).

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A:

Q: 3. 21 ) f(x) = 3x + 1 [1,3] n=3 a=1 right left & middle hand rule b=3

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Q: X 1 2 3 4 f(x) 2,6 3,5 3,2 2,4

A: From the given table, The general formula is,

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A:

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A: As per the question, we will verify the above for f=3x3-2xy2. We are given that xi=1, yi=2; xf=5,…

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A:

Q: If T, is an MVUE of y (0) and T, is any other unbiased estimator of y (0) with efficiency e < 1,…

A: Answer: For the given data,

Q: 2. Show that for simple linear regression (SLR) we have that cov(B, B,) = - xoʻ/S

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Q: Linearize x³ + ln x about x=3

A: Let f(x)=x3+ln x about x=3 f'(x)=3x2+1x Recall: Linearization  L(x)=f(a)+f'(a)(x-a)  we have a=3

Q: 1. Linearize x³ + ln x about x=3 In

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A: Correct answer is (b). There is negative autocorrelation in the model.

Q: || 2)) D3. IS D3 1

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Q: Exercise 1.1: Error Propagation • Suppose x = v3, and x = 1.732 is a floating-point representation…

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Q: from the first principle defferentiate h() = 5x³²x+7 2² +2+1

A:

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A: The chances to catch the train will be as follows-

Q: 4. Let x N (e, 1), n = 2, let T = a. 34+0² 36 b. + 17+0² 36 b. T₂ 4X₂ , RT (0) = C. 34 36 5. Let x…

A: The random variable X follows normal distribution such that X~Nθ,1 A random sample of size n=2 is…

Q: (а) Р(0, 1), t %3 /2 t = (b) Р 2 (с) Р( — 1, 0), t%3D (d) Р 2 2 (е) Р(0, — 1), t 3 () P(- (f) Р 2 /2…

A: a. Given point, P(0,1)

Q: E (x. - x Y Show that is a consistent estimator for o is N (µ, o²).

A: ANSWER: For the given data,

Q: . Let f(x) = ka. Determine the constant a so that f(-1) = 10 and f(2) = 5 19 4

A: Given query is to find the constants of the function.

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A:

Q: Estimate the error if P3(x) = 1 + x +²2² + is used to estimate the value of eª at x = = 1/2.…

A:

Q: Classify the following statements as to whether they belong to the area of DescriptiveStatistics or…

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Q: An M.V.U. is unique in the sense that if T, 1 M.V.U. estimators for y (0), then T, = T, almost

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Q: af Find and əx af dy f(x,y) = (x³-4) (3y + 2) af for the following function.

A: Given query is to find indicated derivative.

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A:

Q: 1 If a parent function x) = is compressed horizontally by a factor of 5, what would be the equation…

A: The horizontal stretch or shrink in the graph of y=f(x) is represented by the transformation…