Find the m.g.f. for triangular distribution defined by f(x) = x₁ f(x) = 2-x. 0≤x≤ 1, 1 ≤ x ≤2.
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- (26) Let X b(8,- Var-x) and distribution function.Varza) (16) Let X =U(3) find x) and distribution function.Show that for the distribution: dF = Yo 1 Hy = 2 a (r-1) a² r+1-2p -P dx ;-a≤x≤ a, 0(26) Let X b (8,-) find Var-x) and distribution function.Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]? (d) Obtain E[Y]. That is, what is the expected value of your 2023 fantasy basketball budget? (e) Golden State Warriors won the 2022 NBA finals. Their estimated 2022 payroll is about $194 million. Would your 2023 fantasy basketball budget be on average larger than Golden State Warriors' 2022 payroll? Explain briefly.Find the distribution function which corresponds to the probability distribution defined by f (x) = 15 for x = 1, 2, 3, 4, 5O Suppose that you enter a fantasy basketball league. Suppose that the 2022 team budget, say X, is randomly drawn from a uniform distribution on the interval [90, 210], where the unit is U.S. million dollars. In addition, suppose that after the value X = x has been observed (90 < x < 210), the 2023 team budget, say Y, is randomly drawn from a uniform distribution on the interval [x, 210]. In other words, the 2023 budget is at least as large as the 2022 budget. (a) For any given value of x (90 < x < 210), obtain E[Y|X = x]. (b) In view of part (i), obtain E[Y|X]. (c) What is the difference between E[Y|X = x] and E[Y|X]?A subway train on the Red Line arrives every 7 minutes during rush hour. We are interested in the length of time a commuter must wait for a train to arrive. The time follows a uniform distribution.Give the distribution of X. find . f(X) = , where ≤ X≤ . μ = σ = Find the probability that the commuter waits less than one minute. (Enter your answer as a fraction Find the probability that the commuter waits between two and three minutes. State "60% of commuters wait more than how long for the train?" in a probability question. (Enter your answer to one decimal place.) Find the probability that the commuter waits more than minutes. Draw the picture and find the probability. (Enter your answer to one decimal place.)Let. X have a uniform distribution on the interval (1,3). What is the proba- bility that the sum of 2 independent observations of X is greater than 5?SEE MORE QUESTIONS