If x, x2 ... Xn is a random sample from N (µ, o²) popula- tion, find sfficient estimator for µ and ơ.

Q: Let X be a random variable with mean E[X] = 20 and variance Var(X)= 3. Define Y = 3 - 6X. Calculate…

A: We have given that, Let X be a random variable with mean E[X] = 20 and variance Var[X] = 3   We know…

Q: uppose you and a friend each take different random samples of data pairs (x,y) from the same…

A: From the given information, It is given that the different samples are taken by you and your friend…

Q: EX7.8) Let Y be a random variable having a uniform normal distribution such that Y~U (2,5) Find the…

A:

Q: Calculate value of (t) if: first sample mean = 85, second sample mean = 91, and o x1-x2 =

A: We want to findvalue of t

Q: Let x , X, ............ X be a random sample drawn from a given population with mean u and variance…

A:

Q: 3 For an SRS {Y: ³;=, from the normal distribution 1 fiy (цілето 2) vivore (y;u, - Show that the…

A: Here, The simple random samples of size n taken from the normal population. We have to show that the…

Q: opulations with mean Hi and variance of (i = 1,2), respectively where u, = 20 , n = 36 and µz = 18,…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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: Suppose Y₁, Y2,, Yn is an iid sample from a gamma population distribution with shape parameter a = 2…

A:

Q: Prob. 3 Let X be a random variable with cumulative distribution function (cdf) given by Fx(x) = {1 -…

A: Let X be a random variable with a cumulative distribution function (cdf) given byTo findThe…

Q: 3. Let x be a random variable representing the concentration of chemical Z in human blood. Over a…

A:

Q: Show that (X1+ X„)/2 is an unbiased estimator of u, if {X1, ... , X„} is a random sample from the…

A: Solution

Q: Let Y, represent the ith normal population with unknown mean , and unknown variance of for i=1,2.…

A: Given that the random variable  represents the ith normal population with unknown mean  and unknown…

Q: Show that the mean of a random sample of size n from an exponential population is a minimum variance…

A: Let X1, X2, …, Xn denote random sample from exponential distribution with θ. The probability density…

Q: Let I be an indicator variable with p(I) = {p , I=1 } {1-p , I=0}. Show that the variance of I is…

A: The mean is calculated as follows: EI=∑I×PI=1×p+0×1-p=p

Q: Let X1, . . . , Xn be iid from Exp(β). Find the distribution of the sample maximum Y = X(n) . Is…

A: Given that , , . . . . ,  be i.i.d. exponential with parameter .i.e.

Q: Let X1, X2,...Xn be a random sample from a Poisson distribution with variance 0. Find an unbiased…

A: Let, X1, X2…Xn be a random sample from Poisson distribution with variance = θ For Poisson…

Q: If X is a Poisson variate such that 4) + 90 P(X=6), find the P(X=2)=9P variance (X =

A:

Q: . Let X1, X2, ., Xn be a random sample from a normal population with mean u variance o?. Xm and Så…

A: Given: X1,X2, ....... ,Xn ~Nμ, σ2Sample mean = X¯nSample variance = Sn2

Q: 8. Let y be a normal random variable with a constant mean E(y) = 4, constant variance var(y.) = o?,…

A: We have given that  Let yt be a normal random variable  E(yt)=μ Var(yt)=σ2 Cov(yt,yj)=0    We have…

Q: A random variable X has only two values a and b with P(X = a) = p , P(X = b) = q (p + q = 1). Find…

A:

Q: Suppose that X1,... X, is a random sample from a normal distribution with mean u and variance o?.…

A:

Q: Q1. Let X; and S be the mean and variance of independent random samples of size n; from populations…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Using a long rod that has length μ, you are going to lay out a square plot in which the length of…

A: If an expected value of sample statistic is equals to the population parameter then that…

Q: Suppose X and Y are two independent variables with variance 1. Let Z = X+bY where b > 0. If Cor(Z, Y…

A: Given that, V(X)= V(Y)= 1 So  V(Z) = V(X+bY)  = V(X)+b2V(Y)  { x and Y are independent} = 1+ b2

Q: Suppose that X₁, X2, . . ., X₁ and Y₁, Y₂ , . . Yn are independent . random samples from populations…

A: Let X=X1,X2,..,Xn and Y=Y1,Y2,...,Yn are independent random samples from a population.Here,  μ1 and…

Q: 6. Show that 1 s2 = TE2-1(Xi – x)² is unbiased estimator of the population variance o?

A: Show that S^2 is unbiased estimator of population variance

Q: The covariance of two perfectly correlated variables X and Y is 96. Determine ox and Oy if it is…

A:

Q: Suppose that X₁, ..., Xn are i.i.d. from a normal population with mean µ and variance o². Calculate…

A: Let X1,X2​,…,Xn​ be independent and identically distributed (i.i.d.) random variables from a normal…

Q: Let A1, A2, A3, ..., An be a random sample with unknown mean Ai = μ, and unknown variance Var(X₂) =…

A: Let Xi be the random sample havingE(Xi)=μVar(Xi)=σ2Define estimatorΘ^=X¯2=(1/n∑k=1nXk)2Concept Used:…

Q: Show that S2 is unbiased for o2. Find variance of S2. Find the bias of ô? and the variance of ô?.…

A: Given that X1, X2,........,Xn follows Normal distribution with unknown parameters. Note : According…