Let X be a  r.v. such that E(X2k) = (2k)!/k! , E(X2k+1)=0 . Find the mgf of X and  also its ch.f . Then deduce the distribution of X.

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A: Given: Distribution Function: fx=12xe-x,    0&lt;x&lt;∞ Raw moments, μ1'=1μ2'=3μ3'=12 Central…

Q: Let X has uniform distribution on [-1,1]. Find E(X|X²).

A: Given: X has uniform distribution on [-1,1]. Then the pdf is: f (x)=12for -1&lt;X&lt;10Otherwise

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Q: For the probability density function f(x) = 3x^2 on [0,1], find: V(X)

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Q: Suppose that the probability density functions of x is 3x2, 0<x < 1) F(xE0, Elsewhere ) a) Determine…

A: Given that,  P.d.f. is f(x)= 3x2, 0&lt;X&lt;1 C.d.f. of X is given by, F(x)= integration|0x f(x)dx

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A: Solution: There is two different question I am solving second

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Q: Let X be a random variable defined by the density function COS --4 <x5 4 fx(x) = {16 8. elsewhere…

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Q: Let X be uniformly distributed over (0,4). Calculate E[X5].

A: Given: X follows Uniform distribution over ( 0 , 4)

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Q: Let X have a Weibull distribution with parameters a and B, so E(X) = B· T(1 + 1/a) V(X) = B?{T(1 +…

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Q: Let X be a continuous random variable with PDFfx(x)= 8/x3, x> 2. Find E[W where W = X/3.

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Q: 2. Show a relation between the beta and the binomial distributions by proving the following relation…

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A: We know that Probability  of uniform  distribution  f(x)= 1/b-a    , a&lt;x&lt;b

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Q: Let X have a gamma distribution (a, ß)and Let Y = ex.Find G(y)and g(y) by D F method %3D

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A: Cumulative Distribution Function  is the probability of occurrence of various events together within…

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A: From the given information, X be a gamma distribution (α,β).

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A: Let X be the continuous random variable with pdf, fX(x)={1θe-xθ; x≥00; otherwise To find E[x],…

Q: Click the icon to view the critical values of the Student's t distribution. Vhich of the following…

A: n = 150 MD = 0.0412 sd = 0.3039

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Q: Show that the function f(t) = -,te Z 21 %3D 5SIS 10, defines a discrete probability distribution by…

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Q: Suppose the joint distribution of the two random variables X1 and X2is given by f(r1, 22) = S6r2, 0<…

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Q: Consider a Uniform distribution defined as fx(x) = 36 2<x <8, %3D еe. w. 1. Find E (). O 0.462 О…

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Q: Suppose that the probability density function of a random variable X is as follows: f(x)= cx,…

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.