1.) Consider the discrete random variable with pmf: P(X=x)=(A/(4^x)), x=2,3,4,5,.... What is the value of A?

Q: Suppose Y₁, Y₂,,Y, is an iid sample from a Poisson(A) distribution, where >> 0. Is Y a consistent…

A: Defination: ȳ is an consistent estimator of λ iff  E(ȳ)=λ as n is large. V(ȳ)=0 as n is large.

Q: The combined amount of time three customers spend waiting to receive service at a drive-through…

A: Solution Given, Gamma distributed random variable with parameter theta = 0.4 per minute. What is the…

Q: The random variable x is known to be uniformly distributed between 0.5 and 2.5. What is the standard…

A: Given,A random variable X~U(a=0.5 , b=2.5)f(x)=12.5-0.5  f(x)=12   ;  0.5≤X≤2.5

Q: In a certain country, the amount of annual rainfall (in tonnes per m) is modelled through a Gamma…

A:

Q: Suppose Y₁, Y2,, Yn is an iid sample from a Poisson(A) distribution, where > 0. Is Y a consistent…

A:

Q: Let X1, X2, ..., X, denote a random sample from the normal distribution with mean u and variance o?.…

A:

Q: Let X,, X2- --, Xn be a random sample from a normal distribution with mean M and variance o Show…

A: The joint pdf of X1, X2, ....., Xn is given as follows: f(x1, X2, ....., xn)=12πσnexp-12σ2∑ixi-μ2…

Q: Show that a beta distribution with α=β=1 is the same as the U (0,1) distribution.

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Q: Suppose that X is a continous random variable taking value between 0 and 1 with the pdf f(x) = 2x.…

A: There is two different question So i am solving first

Q: Show that the random variable X = Z and Y = 2?. fact that they are statistically dependent. are…

A: Answer: Using the given data,

Q: Let x be a Bernoalli random variable with mean of 0.6. Find p (1 \leqx \leq 4 \) اختر احدى الدجابات…

A:

Q: Let X1, X2, ..., X, be a random sample drawn from a distribution with mean u and variance o? and let…

A: (a). Show that X^ is an unbiased estimator of μ: Here, X1, X2, …, Xn be a random sample of size n…

Q: Suppose that Y Еxponential() ~ and let X = exp{-Y/ß} be a new continuous random variable. If…

A:

Q: Suppose X,,X2, . ,X, be iid random samples from Uniform(a, b), where b > a. ... Find the method of…

A: It is given that- X1,X2,....,Xn~Ua, b, b>a So mean and variance are given as, mean = x = a+b2…

Q: What is the pdf of the sum of two random variables each of which each is a gamma distribution with…

A: Solution

Q: Let be a geomerric random variable with prf y=1,2,3... where 9 Find. estimator using matimum…

A:

Q: Suppose that X1, X2, ., X50 is a random sample from a N(300, 25) distribution. With the test Ho: u =…

A:

Q: Derive formulas for the mean and variance of a Poisson random variable with parameter λ using its…

A: The objective is to find the formula for the mean and variance of a poison random variable with the…

Q: Let zand y be two independent Gaussian random variables, both with expected value zero and variance…

A: Given, x and y be two independent gaussian random variables.    We have to find the power spectral…

Q: Suppose Y is a Poisson random variable with rate A. Let X be a random variadie be such that given Y,…

A: It is given that the Y~ Poisson(λ) and X|Y=y ~ Gamma(1,Y) We have to find that the E(X) and Var(X)

Q: Determine the probability that the minimum value in a random sample of size 5 from an exponential…

A: Required Probability = 0.9179 answer   Calculations:

Q: 2. A system consisting of one original unit plus a spare can function for a random amount of time X.…

A:

Q: Let X, X2, .., Xm, be a random sample of size n = 2m + 1 from exponential distribution with…

A: Let X1, X2, ..., Xn be a random sample of size n=2m+1 from exponential distribution with parameter…

Q: A random sample of n volumes in the form of X1, X2, ... , Xn is taken from a population with a…

A: We have to find the log likelihood function for the normal distribution.

Q: Derive the mgf of an exponentially distributed random variable with mean β. Verify that(E[Y])2 =…

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Q: Suppose the random variable X follows an Inverse Gaussian distribution with parameters u and 0. Use…

A: From the given information, the random variable X follows an Inverse Gaussian distribution with…

Q: Let Xi. X2 --- Xn be a random sample from the Poisson _ 8*e¯® distribution . with pmf fix;o)=. Find…

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Q: Let X1, X2,.. , X, be a random sample from a normal distribution with mean 0 and variance 4, let Y1,…

A:

Q: If X1, X2, ... , Xn constitute a random sample from anormal population with μ = 0, show that…

A: It is given that X1, X2, …, Xn is a random sample of the normal population with N(0, σ2). That is,…

Q: Suppose that X1, X2,..., X, constitute a random sample from a uniform distribution in the interval…

A: Given: X1, X2,......,Xn constitute a random sample from a uniform distribution in the interval…

Q: Suppose that X,, X2,...,X, denotes a random sample from a Poison distribution with mean 2. Find the…

A:

Q: Suppose that X1,X2,...,X200 is a set of independent and identically distributed Gamma random…

A: Given: Where i = 1 to 200

Q: i) Let X,X2, be two identical independent distributed (iid)random variables ,each X- X2 having chi –…

A: Hello! As you have posted 2 different questions, we are answering the first question. In case you…

Q: Suppose that Y, Y2,.-.,Y, are independent random variables from a gamma distribution of the…

A:

Q: Suppose s random sample X, X2, ..., X, of size n is taken from a population with p.d.f 1 f(x;0) = e…

A: a. From the given information, fx,θ=1θ+1e-xθ+1, 0<x<∞, θ>-1        =1θ+1e-xθ+1,…

Q: "The central limit theorem states that if X1, X2, X, are independent and identically ....…

A: Solution: 5. a. The statement is “The central limit theorem states that if X1, X2,……..,Xn are…

Q: Two Independent random samples of n observations are to be selected from each of two binomial…

A: Given: α=1-0.98=0.02E=0.05

Q: 2. Let X1, X2, ..., X, be iid random variables with a common pdf/pf f(x, 0) depending on an unknown…

A: Please see the handwritten solution.

Q: The time required to repair a machine is an exponentially distributed random variable with mean of…

A: A machine is exponentially distributed with mean 0.5 hour

Q: Let X1,X2,.,X, be a random sample from f(x;8) = 0e-nI(0,0)(x). Find a 100y or (1 - a)100 percent…

A: Given that,          Let X1,X2,X3,.....,Xn be a random sample            fx;θ=θe-θxI0,∞(x)…

Q: Suppose X1,..., X, are iid gamma random variables with parameters 1 and 0 Let X, = E X; »let Wn log…

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

Q: Show that for a random sample of size 2 from N (0, ơ²) population, E[Xq„] = - o/Vr.

A:

Q: Suppose that the random variables X₁,..., X and Y₁,...,Y, are random sample from independent normal…

A: It is given that Xi~N(3,8), i=1, 2, … , 8, where 3 is the mean and 8 is the standard deviation. The…

Q: Let X1, X2, X3,..., X, be a random sample from a distribution with known variance Var(X,) = o?, and…

A:

Q: The amount of gasoline in gallons sold by three different gas stations during one day is given by…

A:

Q: Sketch the PDF and CDF of a continuous random variable that is uniform on [0,2]

A: Let X be the continuous random variable uniformly distributed in the interval 0 and 2. Thus, the…

Q: Y¯ be the means of

A: Given:

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.