Suppose X has the following probability mass function: p(1) = 0.5, p(2) = 0.3 p(0) = 0.2, Calculate E[X²].
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![Suppose X has the following probability mass function:
p(1) = 0.5,
p(2) = 0.3
p(0) = 0.2,
Calculate E[X²].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bb26c03-de5b-4508-955f-bcd8b5281142%2F4c6c3cef-997b-4dae-ab12-f3a6a1fa5123%2Fbg54wkn_processed.jpeg&w=3840&q=75)
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- Consider the following exponential probability density function. f(x) = 1 5 e−x/5 for x ≥ 0 (a) Write the formula for P(x ≤ x0). 1−E−(X5) (b) Find P(x ≤ 4). (Round your answer to four decimal places.) (c) Find P(x ≥ 5). (Round your answer to four decimal places.) (d) Find P(x ≤ 6). (Round your answer to four decimal places.) (e) Find P(4 ≤ x ≤ 6). (Round your answer to four decimal places.)(c) Let X follow the gamma distribution with pdf S(z) = r(a) on z> 0. If a =1 and V(X)=4 find the value of b, and hence find E(X).4 Consider the following two functions, each having an unknown parameter c. c (x² + 4x + 7) -5 < x < 5 f (x) = otherwise, 100 (x – c)² – 1) -5Consider times at which a parent provisions nestlings, that is, the time be- tween arrivals of a parent carrying food for the nestlings. Suppose that the waiting time between arrivals of a parent bird follows the exponential density function f (t) = 0.6e-0,61 for t z 0 and f (t) = 0 for t < 0, where the waiting times are in minutes. (a) What is the mean waiting time? (b) Find the probability that the wait will be between 2 and 5 minutes. (c) Find the probability that the wait will be at least 3 minutes.If X has a moment generating function (mgf) as A) find the probability mass function of X. B) find the mean and variance of X by using the mgf, M(t), given in the photo C) what is P[X > 1|X > or equal to 0]3. Use the Maximum Likelihood Method to find u for this probability density function: (x - H)2 f (x|µ, 0) = 1 еxp V2no? - 202 a. The likelihood function L is: b. The natural log of the likelihood function is: c. Solve for µ.[2] X is an exponential random variable with variance 9. If (X, Y = (2, otherwise, 1Suppose X has probability density function fx (x) =e for x > 0 and fx (x) = 0 otherwise . Р(2 < X<7) —?[Q1] If the probability density function is f(x) as follows, find: (a) k that makes f(x) a valid pdf, (b) Var(x). Skx*(1- x) 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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