Calculus and Above

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Let X ∼Γ(α,β), which has p.d.f. fX(x)= βα xα−1e−βxI(0,∞)(x),
Let X ∼Γ(α,β), which has p.d.f. fX(x)= βα xα−1e−βxI(0,∞)(x), where Γ(ω):=􏰁∞vω−1e−vdv is the Γ(α) 0 Gamma function, for ω > 0. 1. Compute the moment generating function of X. [5 points] [Hint: 􏰁0∞… read more
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Random variables X and Y are discrete and have the following
Random variables X and Y are discrete and have the following joint CDF: F(x,y) = 1-[(1/3)^x + (1/5)^y]+(1/3)^x(1/5)^y for y = 1,2,... and x = 1,2,... and 0 otherwise. A.) Find Fx(y) B.) Find Fy(y) C.)… read more
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Let X and Y be independent random variables. The pdfs of X
Let X and Y be independent random variables. The pdfs of X and Y are: fX(x) = e−x for x>0 fY(y) = e−y for y>0. FindP(X+Y >1).… read more
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7. Determine the value of if f inverse () =2 and f(x) = 2x^2
7. Determine the value of b if f inverse (b) =2 and f(x) = 2x^2 – 3x +2 8. Given f(x) =|x| , a. Graph g(x) = f (x+3) b. Graph the reflection of g(x) along the line y = x c. State the domain and range … read more
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I am preparing for a probability theory test and I am having
I am preparing for a probability theory test and I am having problems with MGF's these are some examples from previous exams which I would like solutions for along with explanations to help me study. … read more
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1. (a) Use the definition of moment generating functions to
1. (a) Use the definition of moment generating functions to show that if MX(t) is the mgf of a continuous random variable X, then if Y = (X+a)/b, MY (t) = e^(a/b)t MX(t/b)  (b) Choose appropriate co… read more
Expert
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1) A point is generated at random in the plane according to
1) A point is generated at random in the plane according to the following polar scheme. A radius R is chosen, where the distribution of R^2 is X^2 with 2 degrees of freedom. Independently, an angle θ … read more
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Hello, please can you help with this? The question is concerned
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Exam scores were normal in MIS 200. Jason's exam score was
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Solve Uxx+Yxx=0 in the square 0
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Use the rejection method to simulate a random sample of size
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Give a method for generating a random variable having distribution
Give a method for generating a random variable having distribution function F (x) = 1 − exp(−αx^β ), 0 < x < ∞. A random variable having such a distribution is said to be a Weibull random variab… read more
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Use the composition method for simulating from the probability
Use the composition method for simulating from the probability mass function Pr(X = j) = pj,j = 5,6,...,14, where pj =􏰅0.11, whenjisoddand5≤j≤13, 0.09, whenjisevenand6≤j≤14. Write the algorithm, but … read more
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Give an efficient algorithm to simulate the value of a random
Give an efficient algorithm to simulate the value of a random variable X such that Pr(X =1)=0.3, Pr(X =2)=0.2, Pr(X =3)=0.35, Pr(X =4)=0.15.… read more
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Outline the algorithm that generates a random variable having
Outline the algorithm that generates a random variable having a density function f(x) = (x−2)/2 , if 2 ≤ x ≤ 3  (2−x/3)/2 , if3… read more
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Give a method for generating a random variable having distribution
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Consider an exponential distribution with parameter b>0, i.e.
Consider an exponential distribution with parameter b>0, i.e. its pdf is f(x/B) = (1/B) EXP(-x/B) , IF x>=0 . show that the random variable Y=X^(1/L) where L>0 has a Weibull distribution with… read more
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The probability distribution table at the right is of the discrete
The probability distribution table at the right is of the discrete random variable x representing the number of patients waiting outside of a doctor's office. Answer the following: x P(X=x) (a) Determ… read more
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