Problem #1: Let X~ Unif[-2, 2], and Y = (X+ 1)². Problem #1(a): Problem #1(b): (a) Find fy() and fy(4), where fy() is the probability density function of Y. Separate your answers with a comma. (b) Find P{Y < 4}. Enter your answer symbolically, as in these examples Enter your answer symbolically, as in these examples

Q: to STUDENTS of 5さ WHAT FUNCTION =C(x) =

A: Given query is to find the average rate of change form the given function m

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Q: Let X be a continuous random variable with PDF 1 fx(x) for all a E R V27 and let Y = X². Find fy(y).

A: The PDF of X is fXx=12πe-x22, for all x∈ℝ Given Y=X2 We have to find the PDF of Y.

Q: 2. A random variable X has pdf |x| < 1 elsewhere. cx(1+ x) a. Find c. b. Find E{X}and V AR{X} c.…

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Q: Amanda has a von Neumann-Morgenstern utility function given by U= VM , where Mis her income. If she…

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Q: nas a VIN V t, WITETE IS the dm ney won in the lottery. She faces two scenarios: nario 1: With a 50%…

A: Given IBM utility function over money is u,(x) = √x Here, x is the amount of money

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Q: Problem 4) Let X be a continuous random variable with f (x) as its pdf and u as its mean. Prove…

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A: Let  be the amount of time until the next earthquake in California is described by the following…

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Q: If E(X) = 6 and E[(X) (X-1) ] = 51, find the second moment= 1 and the variance of X= 2

A: Given Data: E(X)=6 E[(X) (X-1)]=51

Q: Example 8-20. how that : E( ) = | ta-1 G(t) dt, a > Ó 20 X+a (*) %3D ... shere G(t) is the…

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Q: Exhibit 4 A random sample of 121 bottles of cologne showed an average content of 9 ounces.…

A: Given that  Sample size n =121 Population mean μ =9 Population standard deviation =0.18 NOTE:-…

Q: For the following discrete variable with probability f(x) X 1 3 4 f(x) 0.2 0.15 20 0.05 0.15…

A: We have given that,  X is a discrete random variable having pmf.  X     :    0            1        2…

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A: The PDF of random variable X is given by:We have to find the value of aThe probability…

Q: 2 Let ƒ(x)=x³, g(x)=x³. If it holds (fog)(x)= (gof)(x)?

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Q: The amount of time in hours that a computer functions before breaking down is a continuous random…

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Q: Suppose that g is an easy probability density function to generate from, and h is a non- negative…

A: Given g is an easy probability density function to generate from and h is an non-negative function.

Q: If ƒ = {(1, − 1), ( – 3, 1), (2, the following values of f and g. a. f(1) b. g(2) = = 3 c. g = d.…

A: Given :- f=1,-1,-3,1,2,14,π,1 and g=2,-1,-3,-2,34,-1 To find:- f1 g2 g34 f2 g-3 fπ

Q: 7. Assume that X is a nonnegative, integer-valued random variable with p.g.f. G(z). Let G(¹)(z)…

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Q: Problem #1: Consider a population of moose that grows according to P1+1 = Pt + I, where I, = 28 with…

A: Given the population of moose that grows according to  pt+1=pt+𝕀t   where 𝕀t=28  with a 39% chance…

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Q: Question 23. (a) Use the expectation operator to show that for any random variable Y, Var(Y) = E(Y²)…

A: Solution: Part a) Variance is defined as the average of the squared differences from the mean. That…

Q: Because P(A n B) has been defined as x, and we calculated the value of P(A n B) = P(A) P(B) to be x²…

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Q: Suppose a random variable X has a PDF 1 £x(x) = -ae' -a|z| -∞AXA ∞, 2 where a > 0. This is called…

A: Given:X~L(0,α)f(x)=12αe-α|x|                          ;-∞&lt;x&lt;∞;α&gt;0Find:1. Y=|X|2.Y=X2

Q: 4. Assume the joint PMF given in Problem 1. (a) Find the correlation of X and Y. (b) Find E[X]. (d)…

A: According to the answering guidelines, we can answer only three subparts of a question and the rest…

Q: Let X have the following density. Values of X -2 -1 0 1 Probabilities 0.1 0.2 0.3 0.3 0.1 (i) Derive…

A: i) Formula for E(X): EX=∑XPX Consider, X -2 -1 0 1 2   P(X) 0.1 0.2 0.3 0.3 0.1   X*P(X) -0.2…

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Q: Problem 2. (SW 11.8(a-c)) Consider the linear probability model Y₁ = Bo+B₁X₁+u₁, and assume that…

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Q: (a) If the sum of the deviations of the numbers X1, X2, X3, ....., Xn from their mean, X, is zero.…

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Q: 1-2x (c) Determine the values of a, b and c if =1+ax+ bx? + cx. Hence, by 1+2x, 1 show that 2 s 3,…

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Q: Suppose we roll 2 six-sided dice. Let X be their sum and Y be the larger value of the two. (a) (10…

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Q: 2. P(X = x) =55 x², if x € {1,2,3,4and 5} %3D 0,otherwise 3. P(X = x) = if x € {1,2,3,4,5,6}…

A: Given,  P(X=x)= x2/55  for x= 1,2,3,4,5 Then by substitution,  P(X=1)= 1/55 P(X=2)= 4/55 P(X=3)=9/55…

Q: If two functions are defined as: g: from (1,2,3} to {a,b,c}, and g(3) = a, g(2) = b, g(1) = c h:…

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Q: Problem 3. Suppose XILY, E(X) = E(Y), and their variances exist. Prove that E[(X-Y)2]=Var(X) +…

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Q: Suppose X1,X2,...,Xn is a random sample from a binomial distribution. Recall X is the number of…

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Q: need help with all parts? but esp d)

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Q: 1. What is the probability that an arrival to an infinite capacity 4 server Poison queueing system…

A: Given information: λμ=3P0=110c=4