If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y = X1 + X2 +···+ Xn is a sufficient estimator of the parameter θ.

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Q: Let X1,..., X, be independent such that X;|p ~ Bernoulli(p) with pE (0,1), and p~ Uniform(0, 1).…

A: c) Given that X1,X2,.....,Xn be independent such that Xi|p~Bernoulli (p). f(Xi|p)=pxi(1-p)1-xi…

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A: A quadratic equation is written as f(x)=Ax2+Bx+C. f(x) has real roots if B2-4AC≥0.

Q: (a) Compute E[Z] and Var(Z). (b) Compute Pr(Z> 0). (c) Find the 1* quartile Qi and the 3rd quartile…

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Q: Consider the linear model Y₁ = B₁ + B₁X₁¡ + ß₂X2i + u; where u; is the error term and where E (u;…

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Q: Xy Xy Xn is a random sample from a normal population ...... 2 x², is an unbiased estimator i = 1 P…

A: Answer: For the given data,

Q: 5. Suppose that X is a continuous random variable satisfies P(X > t) = + Be-Ht, t > 0, = ae where a…

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Q: Consider the econometric model y = Bo + B1x +u and the OLS estimator B, for B1. We know that: O…

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Q: Let X1, X2, ..., Xn be an independent random sample from n(µx,ox), and Y1, Y2, . .., Ym be an…

A: Given X1,X2,...,Xn~N(μx,σx2)Y1,Y2,....,Yn~N(μy,σy2) are two independent random samples.   Denote…

Q: Find Pr (0 < X1 <1/3,0 < X2 < ½) if the random variables X1and X2have the joint p.d.f. S(X1, X2) =…

A: From the given information, fx1, x2=4X1(!-X2), 0&lt;X1&lt;1, 0&lt;X2&lt;1 Consider, P0&lt;X1&lt;1/3,…

Q: Let the random variable X and Y have the joint p.d.f. [12xy(1-x) f(x,y)= 0 Find E[X] and Variance o…

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Q: a. Suppose Y; = B1x; + €;, i = 1, ..., n. In this equation x is non-random, B1 is a parameter…

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Q: Given y = fo + Bix+ B2x² + B3x + u, the null hypothesis (Ho) that the regression is linear in x'and…

A: Given information: The given regression equation is: y = β0 + β1x + β2x2 + β3x3 + u.

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Q: 47. Let X1, X2, ., Xn be a sample from any population with parameter 0 and T, and T2,n be any two…

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Q: Let X and Y be continuous random variables with joint p. d. f. f(x, y) = {2 if 0 <y<1-x;0 <x<1…

A: The joint probability density function is fx, y=2 if 0&lt;y&lt;1-x ; 0&lt;x&lt;10, elsewhere

Q: 1. Find the uncertainty equation for the following function f, assuming x, y, and z are variables.…

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Q: Let X and Y be two (continuous or discrete) random variables with E(X)=D2, E(Y)3D5, Var(X)=9,…

A: Given: E(X) = 2 E(Y) = 5 Var(X) = 9 Var(Y) = 16 Cov(X,Y) = 5 Formula Used: Var(X-Y) = V(X) - V(Y) -…

Q: 2. Suppose X1, X2, ..., Xn be a random sample from the following pdf: 1/2 f(2\4, A) = ()" exp[-\(x –…

A: It is an important part of statistics. It is widely used.

Q: Let X1,· , Xn be iid with population density x > 8, fx (x) = {de- otherwise. Here d,0 are unknown…

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Q: Consider a random sample X1, X2, ..., X, from Bernoulli's distribu- tion B(1, p). Prove that X; is a…

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Q: Suppose X is a discrete random variable and has the moment generating function 1 3 2 1 Mx(t) = :…

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Q: Suppose the random variable X has pdf K exp 12V/28 XP ( - ("=2)²). fo 2√/2K 0. £x(u) = 0≤u≤ 4,…

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Q: If Y is an exponential random variable with parameter , then μ = E(Y) = 8 and o² = V(Y) = 8². The…

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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: 7.5.7 Over the circle X² + Y²s*, random variables X and Y have the uniform PDF ,ک شو + ل ("r)/1]…

A: Step 1: Given that the joint pdf is,                                           We have to…

Q: Let X1,X2,... be a sequence of identically distributed random variables with E|X1|<∞ and let Yn =…

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Q: y 1 2 4 8 16 p(y) 0.05 0.10 0.35 0.40 0.10

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Q: In order to obtain a good linear approximation for In (7.4) what would a particularly useful nearby…

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Q: (iv) Find the Fisher information in this sample of size n about the parameter 8.

A: It is given that Xi, i = 1,2,......,n follows N(0, θ) (due to form of given pdf), then E(X) = 0 and…

Q: Let X be a random variable with the moment generating function M(t) = 1/(1 – t)², t<1. Find E(X³)…

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Q: Show that if t" = (t+t) where t and ť are both most efficient estimators with variance v, then var…

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Q: Suppose the random variable X has pdf K 2√/27 (xp ( - (a − 2)²) - £x(u) = 0 ≤u≤ 4, otherwise. where…

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Q: Let Xi. ---- Xnd Glle e) and Tet TX = Exi , a) show tha T) is unbiased estimator for WcO) =nG: E…

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

A: Answer: For the given data,

Q: An insurer has data on losses for four policyholders for 7 years. The loss from the th policyholder…

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Q: Let X1, X2, . . . are independent indicator variables with different probabilities of success. That…

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Q: Let X and Z be two discrete-valued random variables. Suppose E(Z|X the specific form = x) is a known…

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Q: a) Find the marginal pdf's of X1 and X2 b) Are X1 and X2 independent? Why or why not? c) Find P(X1 <…

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Q: Theorem 11. Let X be a random variable and let g(x) be a non-negative function. Then for r > 0,…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.