Let X₁ ~ exp (0.5) X₂~ exp (2) X₂ ~P (2, 3) with corresponding pdf f, (x) in the interval [0, 1) falu).. [63]
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please note that x~p(2,3) is a pareto distribution.
![Let X₁~ exp(0.5)
X₂ ~ exp (2)
X3~P (2, 3)
with corresponding pdf f, (x) in the interval [0,1)
falu)--
[63]
FBz (₂) -- [3, ∞)
so that each interval has a probability constant
of one-third
Determine the spliced distribution
so that its
pdf is continuous without imposing equal probabilitie](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc6ce5534-2387-4074-a910-302bb6e31c8a%2F90d27dc6-d346-4f4f-b11d-28ef1548b550%2Fj10x8vh_processed.jpeg&w=3840&q=75)
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- Let X₁, X₂ be IID with \Exp(1), the standard exponential distribution. Show that Z = X₁/X₂ has an F-distribution. Determine the degrees of freedom of this F- distribution.If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?Let X be a continuous random variable with a pdf given by f(x) = (3x^2)/2 where x lies in the closed interval [-1,1]. Evaluate P(x>1/2). Select the correct response: 7/16 8/17 2/17 7/8
- Suppose X is a random variable whose pdf is given by f(x) =k(4x-2x^2) 01)Find the mean of the random variable X with PDF S 3x² _if 0Identify the distributions of the random variables with the moment- generating functions shown below. For each random variable also indicate what the mean and the variance are. a) m(t) = e^2.2(e^t−1)b) m(t) = 1/(1 − 2t)^2 c) m(t) =( e^5t−e^t )/4tIf the probability density function of X is f(x)= 2xe-x² for 0Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{OTwo random variables X and Y have joint char- acteristic function l@,,m)=exp(-20,?-80;) (i) Show that X and Y are zero mean ran- dom variables.Suppose that f(x)=2/(3^x), x=1,2,3,... is the probability function for a random variable X. Find P(X>3). Use 4 decimal places.For the continuous probability function f (x) = Kx² e* when x20 fint i) k i) mean iii) varianceA college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X = the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is as follows. The pdf is f(x) = kx^2 if 0 <= x <= 2, and 0 otherwise. (a) What is the probability that the lecture continues beyond the hour for between 30 and 45 sec? (Round your answer to four decimal places.)SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON