The characteristic function for a Gaussian random variable X, having a mean value of zero, is ¢, (@) = exp Find all the moments of X using ø,(@).

Q: how to find E(X), E(Y), E(X^2)

A: Given that X and Y are independent and follows N(0,1)

Q: A random variable X has the following PMF: [refer to image] a) Find E(X) b) If Y = g(X) = X^2,…

A: The PMF of X is given as:

Q: Find the PSD of a stationary random process for which Auto correlation is RYx (t) 6 e- alt|

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Q: The input voltage to a rectifier is the continuous uniform (-1, 1) random variable U. The rectifier…

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Q: 02 Find the moment m22.

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is Cor(X,Y)=−34.…

A: Formula used Var ( X+Y) = Var(X)+Var(Y)+2Cov(X,Y)

Q: fx(x) = {{ √ x/2 01 Let Y be the output of the "clipper": Find: a) The probability P[Y = 0.5] b) The…

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Q: Consider random variables X1, · · · Xn, independent and identically distributed such that each Xi ∼…

A: X~N(0,1)

Q: Find the nth moment of uniform random variable and hence its mean.

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Q: generating function M,(t) = 2 determine the 2-t variance of X.

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Q: Let X1, X2, ..., Xn ~ exp(A) be a random sample. Show that X is sufficient for 1/A.

A: Given:  X1,x2,.....xn from exponential distribution with parameters lambda  Then to show that xbar…

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 x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

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 x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance…

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Q: Suppose that the random change in value of a financial asset is X over the first day and Y over the…

A: The variance of X+Y is calculated asVarX+Y=VarX+VarY-2CovX,Y

Q: Let X be a random variable and a real number. Show that E(X - a)² = varX + (µ − a)² Hereμ = EX is…

A: E(X−a)2=E(X−μ+μ−a)2=E((X−μ)+(μ−a))2=E((X−μ)2+2(X−μ)(μ−a)+(μ−a)2)=E(X−μ)2+E(2(X−μ)(μ−a))+E(μ−a)2=E(X−…

Q: Let x be random variable with E(x) = 2 and var(x) = 3. Verify that random variable x and the random…

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Q: Let X be a random variable with the function, -(x-4) for x > , Let f (x)={ elsewhere. Derive u and…

A: Given that X is a random variable with probability density function; f(x)=e-(x-λ), for x>λ0,…

Q: The PDF of the random variable XX is given below (1st figure). Suppose you have a random variable Y,…

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Q: Derive the MGF for an exponential random variable X ~ exp(A) (try the Kernel trick!) O eta t-入…

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Q: Find kurtosis using quartile deviation.

A: Given : Marks :  74 29 69 66 62 53 51 44

Q: Suppose that X and Y are independent random variables with EX=EY=100, and E[min(X,Y)}=79. Find…

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Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: the random variable Y is such that : E(2Y+3)=6    and    Var(2-3Y)=11 find      E(Y^2)

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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…

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Q: If a random variable X has the moment generating function Mx (t) = 2 - ť Datermine the variance of…

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Q: The random variables X,Y have variance Var(X)=36 and Var(Y)=1 and their correlation is…

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Q: exponential

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Q: Find auto-correlation function of a random process whose power spectral densis is given by 1+ 4

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Q: Let the random variable X be defined on the support set (1,2) with pdf fX(x) = (4/15)x3, Find the…

A: The given pdf is shown below:

Q: Let X be a random variable and Y = aX + b with a ̸= 0. Show that the correlation between X and Y is…

A: Given data: Let X be a random variable and Y = aX + b with a ≠ 0. To show: Show that the correlation…