1. Consider estimator g(n) = In(1 – În). Is it consistent for g(p)? Why? 2. Find the distribution of n(g(In) – 9(p)) a n → o.

Q: A random sample of X1,X,, X,...,X, have mean E(X,)= µ and Var(X,)=o². Given the value of §² ¿(x, -…

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Q: 4 The random variable X has p.d.f. 1 f(x) = for -2 <x<4 = 0 otherwise. (i) Sketch the graph of f(x).…

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Q: Suppose the random variable X has pdf Exp(- (u - 2)²), fx(u) = K 2√2π 0≤u≤ 4, otherwise. where K is…

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Q: 16. Show that for the chi-square distribution 1 2 2. 1 f (x³) d (x³) = X (x) e 2n/2 r n/2 H (about…

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Q: 12. Find the moment generating function of the random variable X, having p.d.f. х, for 0<x<1 f (x)…

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Q: 1. Let X be a Poisson random variable with parameter A. Derive E(X) and E(2x)

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Q: (ii) If X is a Poisson distribution such that 2 P(X = 0) + P(X=2) = 2P(X= 1). find E(X). %3D %3D

A: It is given that,  70% of the tiger inoculated with serum are protected from a certain disease i.e.…

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A: From the given information, 1) An estimator are said to be unbiased if E(x) =µ. Hence, it is…

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: Suppose X is a continuous random variable with proposed pdf f(x)=cx for 0<x<2 a) Determine the value…

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Q: 12. Let a random variable X has a geometric distribution with p.d.f. f(x) = pq*", k =1,2,3,. Show…

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Q: Suppose that X is normally distributed with u = 10 ando 2. Find P(IX 10|S3)

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Q: (b) Suppose that the random variables X and Y have the joint p.d. f. f(x, y) = {kx(x – y),0 < x <…

A: Given : f (x , y) = kx x - y  , 0&lt;x&lt;2 , -x&lt;y&lt;x0                  ,    elsewhere (i) To…

Q: 2. Suppose the reaction temperature X (in°C) in a certain chemical process has a uniform…

A: As per bartelby guideline expert have to answer first three subparts only dear student please upload…

Q: (b) Suppose that the random variables X and Y have the joint p. d. f. f(x,y) = {0 Skx(х — у),0 < х<…

A: i) We know that the total probability is 1.So, ∫02∫-xxkx(x-y)dydx=1or, ∫02∫-xxkx2-kxydydx=1or,…

Q: 7. Suppose random variables X and Y are independent. Let g(z) and h(y) be any bounded measurable…

A: The Given Random variables X and Y are independent. To show that CovgX,hY=0.

Q: 11.43. The number (x) of items of a certain kind demanded by customers follows the Poisson law with…

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Q: If a random variable X has a discrete uniform distribution. fx(x)=1/k for x=1,2,..,k;0 otherwise.…

A: From the given information, let X be a discrete uniform distribution. The probability mass function…

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

A: The smaller the variance of an estimator, the more efficient it is. Among the two estimators if one…

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. For any random variable X for which E(X) and E(X²) are finite, show that Var(X) = E(X²) – [E(X)]²…

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Q: 2. (a) If Z = aX + bY and r is the correlation coefficient between X and Y, show that of a*ož + b'ož…

A: Given: Z=aX+bY  r=correlation coefficient between X and 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: Suppose X is a continuous random variable with p.d.f. fX(x) = kx2(1 − x) if 0 < x < 1. (b) Find the…

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Q: Q1/ Let X be a random variable having P. m. f ? P,(X) 1-find C.d.f. of X? 2-Graph the C.d.f.?…

A: Given information: X is a random variable with the probability distribution table as: X 0 1 2 3…

Q: 1. Under Ho, the likelihood function is given by L(Î.) %3D A. True O

A: Let xi; (i=1,2,...,m) be a random sample of size m from a population with probability density…

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: If øx(@) is a characteristic function of a random variable X, then , (co) = 6, (@), where c is a…

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Q: Ql: a) Suppose that Y,.,Y, represent a random sample such that E(Y,)= u, E(Y} )= µ; , E(Y*)= 4. Show…

A: a)

Q: Suppose X has probability generating function GX(t) = 0.2 + 0.3t + 0.1t2 + 0.4t3. What is P(X = 2)?…

A: PGF of a Random Variable is given by, Gx(t) = Σ tx P(X=x)

Q: No. 2 2. If X-N(u-3, ²-2). Find the distribution of the following: C. V = 2-4X 5

A: To find the distribution the step is to express the transformed random variable as a linear…

Q: Example 17:1. X, X2... Xn is a random sample from a normal population N(u, 1). 1 E x?, is an…

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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…

A: We have given that Y is an exponential random variable with parameters beta then mean = E(Y) = β…

Q: 12.14. The chi-squared test can be used to test how well a set of measure- ments (xi, yi) of two…

A: a) Make a table of the observed and expected values of yi. From the given information, , Here, A=50…

Q: Express in words what the random variable Xm9-1 represents (Hint It is the length of which renewal…

A: given that P{X(subscriptN(t)+1) &gt;= x}&gt;= F(x)but by defnition of F(X) = p(X&lt;=x) ,here…

Q: Consider the following three estimators of 0: 6 = the MLE of 0, n+1 n+ ô, = " x Xman x max(X1, ...,…

A: Relative efficiency of θ^2 wrt θ^3; Var(θ^3)Var(θ^2).The uniform distribution has,…

Q: 1- Given a single observation x(0) from a uniform distribution [0,1/0], it is desired to estimated…

A: Here we have given that a single observation x0 form a uniform distribution U0,1θ. Since, U0,1θ is a…

Q: Let X₁ and X₂ be the payoffs of two investments with E(X₁) = E(X₂) = 10. The expectation of the…

A: Given, X1 and X2 be the payoffs of two investments with EX1=EX2=10.

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: 9.3 Let Y1, Y2, ..., Y, denote a random sample from the uniform distribution on the interval (0, 0 +…

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Q: Let X1,., Xn be independent and identically distributed random variables with Var(X1) < o. Show that…

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Q: Let X, (i 1,.,n) be a random sample from the N(4,02) population with unknown ameters u and o2. Then…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: #4: Suppose that X1,... , X7n is an i.i.d. random sample drawn from a U[a, 1] uniform distribution,…

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Q: Let X be a positive random variable (i.e. P(X 1/E(X) (b) E(-log(X)) > -log(E(X)) (c) E(log(1/X)) >…

A: Expectation of a Discrete Random Variable: The expectation of a discrete random variable X, denoted…

Q: Example 3: If x1, X2 , ... , Xn is a random sample from a normal population .2 N(µ,1), show that t=-…

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Q: Help asap!

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Q: Let x1, X2, ..., Xn be a random sample from a continuous uniform distribution with domain (0,b).…

A: Here,  Given that,x~U(0,b)fx(x)=1b, 0&lt;x&lt;b0    otherwise