If X, and X2 are the means of independent random sample of sizes n and n2 from a normal population with the meanu and the variance o².The minimum variance of the estimator w.X + (1 – w). X2 is

Q: Suppose that x,, X, ..., X and Y,, Y,, ..., Y, are independent random samples, with the variables x,…

A: Given  Xi~ N(μ1,σ12) and Yi~N(μ2,σ22 )

Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x= 0 (ii) 1sx<4 ca eor…

A: Given that, The variance of a Poisson variate is 3

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: and X, be independent normally distributed random variables. X,has a normal distribution with mean 1…

A: Introduction - Z-score  z=x-μσwhere , μ=population mean x=score σ=standard deviation +

Q: If X1, X2, ... , Xn constitute a random sample of size nfrom a geometric population, show that Y =…

A: Factorization Criteriom ( Due to Fisher)Let x⏟= (x1, x2,.....,xn) be a R.S from PME f(xiθ).…

Q: 2) Let G and H be two independent unbiased estimators of θ. Assume that the variance of G is two…

A: An estimator T of θ is said to be unbiased if Expectation of T is θ i.e., E(T) = θ Variance of T is…

Q: Example 17-8. X1, X2, and X3 is a random sample of size 3 from a population with mean value u and…

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Q: hemical supply company currently has in stock 100 lb of a certain chemical, which it sells to…

A: Given: x 1 2 3 4 p(x)       0.3     0.5     0.1     0.1

Q: If X is an exponential random variable with parameter 1, and c > 0, show cX is expor

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Q: The random variables X₁, X2, and X3 are Stochastic Independent with respective means 9, 4, and 16…

A: Consider three random variables X1, X2, X3, where, X1 have mean µ1 and variance σ12, X2 have mean µ2…

Q: For every a, 0 > 0. i) Derive the expected value of X. i) Derive the variance of X.

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Q: If X is a Poisson variable such that P(X= 2) = 9P(X = 4) + 90P(X=6), find the mean and variance of…

A: Let X be the random variable from Poisson distribution  with P(X=2) = 9P(X=4) + 90P(X=6)  Then,  We…

Q: A simple random sample of size three x1, X, and x3 is drawn from a population with mean u and…

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

Q: Let X ∼ U(a, b). Use the definition of the variance of a continuous random variable (Equation 2.38…

A: The mean of X is given by:

Q: A random variable X is normally distributed with a mean of 100 and a variance of 100, and a random…

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Q: Consider a random sample Y1,Y2, ., Y, from a population with mean µ and variance ơ². Calculate the…

A: Given that Y1, Y2,....,Yn from a population with mean μ and variance σ2. M^=1197Y4+3Y5+7Y7+2Y19…

Q: Example 17-8. X1, X2, and X3 is a random sample of size 3 from a population with mean value u and…

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Q: Example 17-21. Show that X = 2 X¡ / n, in random sampling from i= 1 %3D exp (-x/θ , 0 < x < ~ f(x,…

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Q: B) Let the random variable X have the moment generating function e3t M(t) 1- t? for -1<t < 1, What…

A: Solution

Q: A chemical supply company currently has in stock 100 Ib of a certain chemical, which it sells to…

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Q: Given W = (ax + Y)² where X and Y are zero-mean random variables with variance o²x =2, and variance…

A: W=aX+Y2 σx2=2σy2=16r=-0.2 X and Y are zero mean random variables.

Q: 7.9 Let X1,...,Xn be iid with pdf f(x|e) : * 0 0. Estimate 0 using both the method of moments and…

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Q: 2. 2 For the random variable Y with pdf f-V)-+v.os y s1,0 else, (a) Find the expectation E(Y) and…

A: The probability density function (PDF) for a random variable gives the probability at each possible…

Q: Let X1, X2, .., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we…

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Q: Given W = (aX + Y)2 where X and Y %3D are zero-mean random variables with variance o2X =2, and…

A: Consider the provided question, W=aX+Y2  where X and Y are zero-mean random variables with variance…

Q: If X1 and X2 constitute a random sample of size n = 2from a Poisson population, show that the mean…

A: Sufficient Estimator: An estimator is said to be sufficient, if the statistic used as an estimator…

Q: Suppose that X and Y are independent random variables with finite variances such that E(X) = E(Y).…

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Q: f X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find…

A: Given:    X1, X2 are two independent exponential random variables with respective parameters λ1 and…

Q: A chemical supply company currently has in stock 100lb of a certain chemical, which it sells to…

A: We have given that,  X be the random variable having probability mass function (p.m.f),    X   :-…

Q: A chemical supply company currently has in stock 100 lb of a certain chemical, which it sells to…

A: E(X) is calculated as: E(X) = ∑xipxi V(X) is calculated as : V(X) = E(X2)- [E(X)]2 ∑xipxi

Q: 14. If t is the most efficient estimator and ť is a less efficient estimator with efficiency e and p…

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Q: If the variance of a Poisson variate is 3. Find the probability that, ne (1) x =0 (ii) 1Sx<4 eor…

A: GivenThe variance of a poisson variate is 3in poisson distribution the parameter of mean and…

Q: X and Y are independent random variables, each exponentially distributed with a mean of Find P{X >…

A: GivenTwo exponential distributions X, Y with mean 110 I exponential distribution Mean =1λ=110⇒λ=10So…

Q: 5. Suppose that X1, X2, ... , Xn are an iid sample from the distribution given below, f(X)e =…

A: Let X1,X2,...,Xn be a random sample of size n with probability density function(pdf) f(x) then the…

Q: If a random variable X has the moment generating function Mx (t) = 2 - ť Datermine the variance of…

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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: a) b) c) Show that for any &> 0 and S, ===₁ X₁, lim P(|S₁ − 0| ≥ ɛ) = 0. 1110 Show that a statistic…

A: As per bartleby guidelines we can solve only first three subparts and rest can be reposted

Q: If has a Poisson distribution such that P(X 21)=0.8646 then then the variance of is equal to

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Q: 3x (1+х) Q2. If f(x) = ; 0<x <2 denotes the pdf of a continuous random variable, find mean 14 and…

A: Mean = E(X) = ∫xf(x)dx Variance = E(X2) - E(X)2 Where ,   E(X2) = ∫x2f(x) dx

Q: 11. Suppose X and Y are independent continuous random variables uniformly dis- tributed on the…

A: Given information X and Y independent continuous random variables follows uniform distribution  0 ≤…

Q: Let X be a random variable with mean μ and variance _2. Show that E[(X − b)2], as a function of b,…

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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: i) If U, and U2 each have a normal distribution with mean 0 and variance 20². Furthermore, mu, (t) =…

A: Given that, U1 and U2 are two random variables follow normal distribution with mean 0 and variance…

Q: Suppose that index model for Stocks A and B is estimated from excess returns with the following…

A: Residual variance is also called as unexplained variance or error variance. It is the variance of…

Q: . Let X be a random variable such that E[X] = 0 and P(-3 < X < 2) = 1/2. Find a non-trivial lower…

A: Here, we have,  E[X] = 0 P(-3&lt;X&lt;2) = 1/2  Now, P(-2&lt;X&lt;2) = 1/2 (Since, X cannot be…

Q: A chemical supply company currently has in stock 100 Ib of a certain chemical, which it sells to…

A: Given, X 1 2 3 4 P(X) 0.3 0.5 0.1 0.1

Q: If X1, X2, and X3 constitute a random sample of sizen = 3 from a Bernoulli population, show that Y…

A: X1,X2,X3 are same from a Bernoulli distribution. Y=X1+2X2+X3 Let X1,X2,X3 are from Bernoullip.

Q: 5. Let X1,X,.., X, is the random samples from U (0,0). Three estimators for parameter 0 are given…

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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.