1. The probability mass function of a discrete random variable X is defined by , x = 0,1,2,3, 1+ kx S(x) = 22 , otherwise. (a) Obtain the value of the constant k. (b) Write down the probability distribution of X. (c) Find E(X) and Var(X) (d) Calculate the values of E(11X – 4) and Var(11X - 4).

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A: It is an important part of statistics. It is widely used.

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A: Given, Two random variables X and Y such that X~Exp(0.5) and Y|X=x ~N(5,x2)

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A: The following table shows the provided outputs of the discrete random variables, along with the…

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A: Given,E(X)=2Var(X)=4we know that…

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A:

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A: Please note that as per our guidelines if multiple questions are posted we can answer the first…

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A: The question is asking whether the product of the expected value of a non-negative random variable X…

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A: Probability Mass Function :- If X is a One-dimensional discrete random variable taking at most a…

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A: Please see the next step for solution.

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A: As per the Bartleby guildlines we have to solve first three subparts and rest can be reposted....…

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A: Given,f(x)=ax+b   ;  0≤x≤1E(X)=23

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A: Given-Mean of X0​: 2X01​+X02​​Mean of V: 2V1​+V2​​The mean of X(t)…

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A: From the given information, the pdf of the random variable X is,

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A: 1. **Definition of Variance**: The variance of a random variable X is defined as:  Var(X) = E[(X -…

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.