Please do it correctly and neatly fast pls 3. Suppose that X is a discrete random variable with the following probability massfunction where 0 <0 <1 is a parameter:X1P(X)20/3 0/32(1 – 0)/3(1 – 0)/3The following 10 independent observations were taken from such a distribution:(3,0, 2,1, 3, 2, 1,0, 2, 1).(a) What is the method of moments estimate of 0?The theoretical mean is:3E(X)Σap ().r=020+1x32(1 – 0)+ 3 x3(1 – 0)= 0 x+ 2 x3= 7/3 – 20%3D

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Answered: (a) What is the method of moments…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Let X be a Poisson random variable with E(X) = 3. Find P(2 < x < 4).
If Y is a discrete random variable with possible values of 1, 2, and 4, and the probability mass function is given by P(Y = 1) = 0.2, P(Y = 2) = 0.5, and P(Y = 4) = 0.3, what is the variance of Y?
Consider a real random variable X with zero mean and variance σ2X . Suppose that wecannot directly observe X, but instead we can observe Yt := X + Wt, t ∈ [0, T ], where T > 0 and{Wt : t ∈ R} is a WSS process with zero mean and correlation function RW , uncorrelated with X.Further suppose that we use the following linear estimator to estimate X based on {Yt : t ∈ [0, T ]}:ˆXT =Z T0h(T − θ)Yθ dθ,i.e., we pass the process {Yt} through a causal LTI filter with impulse response h and sample theoutput at time T . We wish to design h to minimize the mean-squared error of the estimate.a. Use the orthogonality principle to write down a necessary and sufficient condition for theoptimal h. (The condition involves h, T , X, {Yt : t ∈ [0, T ]}, ˆXT , etc.)b. Use part a to derive a condition involving the optimal h that has the following form: for allτ ∈ [0, T ],a =Z T0h(θ)(b + c(τ − θ)) dθ,where a and b are constants and c is some function. (You must find a, b, and c in terms ofthe information…
If X and Y are independent Poisson random variables with E[X] = 3 and E[Y] = 2, what is P[ X = 2 | X + Y = 4 ]?
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A poisson random variables has f(x,3)= 3x e-3÷x! ,x= 0,1.......,∞. find the probabilities for X=0 1 2 3 4 and also find mean and variance from f(x,3).?
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If Z is a discrete random variable with possible values of -1, 0, and 1, and the probability mass function is given by P(Z = -1) = 0.4, P(Z = 0) = 0.3, and P(Z = 1) = 0.3, what is the standard deviation of Z?
Suppose X1, X2, X3, X4 be i.i.d. normal random variables with mean 0 and variance sigma^2, where sigma^2 is the unknown parameter. Consider the following estimators: T1 = X1 - X2 + X4, T2 = 1/3(X1 + X1 + X4), T3... T4... T5 = 1/2|X1 - X2| (a) Is T1 unbiased for sigma^2, for i = 1,2,3,4 (b) Among the estimators T1,...,T4 for sigma^2, which has the smallest MSE? (c) Is T5 unbiased for sigma? If not, find a constant k so that k*T5 is unbiased for sigma^2. Evaluate the MSE of T5.
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