1. Let X be a random variable denoting the rate of return on the fund BancABC. The distribution X is N(u, o"). (a) Define VaR (X), where a e [0, 1].

Q: Y1 0 zero elsewhere. Find E(Y1)

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Q: The distribution of the random variable X is determined by the function: f(x) = ((x-1)2)/c ; for…

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Q: X is a normally normally distributed variable with mean µ = 30 and standard deviation o = 4. Find a)…

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Q: Let X be a continuous random variable whose moment generating function is 4x(t) = (³.) ³. Find Var…

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Q: 1. Consider the cumulative distribution function for a continuous random variable X, if r 1 What is…

A: Given: The cumulative distribution function is as follows F(x) = x3     0< x < 1

Q: Let X1,.. X„ be n independent random variables with PDF fx, (x) = - [A,e- if x > 0, i = 1,2, ..., n.…

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Q: 1. Random variable X has p.d.f 6e-6z I>0 fx(x) = %3D otherwise and let Y = eX. (b) (i.e. Calculate…

A: Probability density function gives the probability at each possible value of random variable X. The…

Q: (a) Find E(XY) (b) Let U = X, V = Y/X. Show that U and V are independent

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Q: X is a normally distributed variable with mean μ = 35 and standard deviation σ = 5. Find a) P(x 21)…

A: given that information x is a normally distributed variable with mean μ = 35 and standard deviation…

Q: i) Find the cumulative distribution function (CDF) of X. 8 ii) Show that the moment generating…

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Q: Let X ∼ N(2, 4). (a) What is the distribution of (X−2) /2 ?

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Q: X is a normally distributed variable with mean μ = 35 and standard deviation σ = 5. Find a) P(x 21)…

A: Given problem Given that   X is a normally distributed variable with mean μ = 35 and standard…

Q: (b)A random variable is defined as 172⁄(3X+1); X = 0 ,1,2,3,4,5,6. Construct the PDF of X, and…

A: Question: A random variable is defined as 172⁄(3X+1); X = 0 ,1,2,3,4,5,6. Construct the PDF of X,…

Q: Then the variance of Y is

A: Given, E(Y/X=x)=2xvar(Y/X=x)=4x2 f(x)=1, 0<x<10, e.w

Q: Let X a b(4,) find Var(3x) and distribution function.

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Q: Q. 1 (i) Find moment generating functions (mgf) of the following probability distributions. (ii)…

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Q: For the continuous probability functionf(x) = Kx when x20 find

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Q: 5. Suppose that X~U(a, b), where U represents a continuous uniform distribution; that is, the pdf of…

A: X is continuous uniform distribution in the interval (a,b). X ~ U(a,b) So, Variance of X, Var(X) =…

Q: 3. Let X be a random variable that is uniformly distributed on the interval (a, b). Find its moment…

A: Moment Generating Function for a random variable X is given by,  E(etX) = ∫-∞∞etxf(x) dx where f(x)…

Q: Let X₁, X₂ be IID with \Exp(1), the standard exponential distribution. Show that Z = X₁/X₂ has an…

A: Let X1 , X2  be the iid random variable having exp(1) Then show that Z=X1/X2 has F distribution…

Q: Find the values of constants 'a' and b' such that Fx (x) = [1-a ·e*/b] u (x) is a valid distribution…

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Q: 3.For the continuous random variable X with probability density function defined by ¤(2 – x) 0 <x <…

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Q: 2. Let f(x) = 3x(x² − 1)(x³ + 2x + 3) (a) Use distribution to expand the function. (b) Use the rules…

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Q: T has an exponential distribution such that P(TS2)=2P(T>4) What is Var(T)=

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Q: 5. Let X be a random variable with the PDF f(x) = r - 1| for 0 0.5) (c) Calculate E(X) and Var(X)

A: The pdf of X is

Q: Let X be the arrival time in minutes of the next red traffic light on a certain delivery route. We…

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Q: 5. Find the moment generating function of the exponentially distributed random vari- able with pdf…

A: Let X be the random variable that follows Exponential distribution.The pdf of X=x is,

Q: Why the probability P(X=x)=0, for a continuous variable,?

A: Given info: The probability P(X=x)=0, for a continuous variable

Q: 2. If the random variable Xhas the probability density function ƒ(x) = ³(1 − x²), −1 < x < 1, what…

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Q: EN Q5 If Pdf of It is given by 0-9 e/sx f(x)= i) e ii) distribution function. find iii) (v) P(X>1)…

A: The pdf of X is given by f(x) = e/√(x) , 0 &lt; x &lt; 4 Note: According to our guidelines we are…

Q: Let X,Y be i.i.d. random variables from U(0,1) distribution. (a) Give the joint distribution of X+Y…

A: From the given information, X and Y are i.i.d random variables from U(0, 1). That is, fx=1,…

Q: Q6. (a) Let X; (i = 1, ..,n) be independent random varables E(X;) = u and var(X;) = of (i = 1, .,n).…

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Q: et X(1) 0. a) Show that X and X) - X() are independent for any s>r. p) Find the distribution of…

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Q: Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation…

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Q: a) You throw two fair dice labeled 1, . . . , 6 independently of each other and let X be the minimum…

A: a) The possible out comes of rolling a pair of die are, Let 'x' be the minimum of the ordered pair.…