The probability density function of a random variable is kx3 f(x) = if 0
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- I need the answer as soon as possibleQ2 Let (X₁, X₂) be jointly continuous with joint probability density function = { -(x₁+x2), f(x₁, x₂) = x1 > 0, x₂ > 0 otherwise. Q2(i.) Sketch(Shade) the support of (X1, X₂). Q2 (ii.) Are X₁ and X₂ independent random variables? Justify your answer. Identify the random variables X₁ and X₂. Q2(iii.) Let Y₁ = X₁ + X₂. Find the distribution of Y₁ using the distribution function method, i.e., find an expression for Fy, (y) = P(Y₁ ≤ y) = P(X₁ + X₂ ≤ y) using the joint probability density function (Hint: sketch or shade the region ₁ + x₂ ≤ y) and then find the probability density function of Y₁, i.e., fy, (y). Q2(iv.) Let Mx, (t) = Mx₂ (t) = (¹, for t < 1. Find the moment generating function of Y₁, and using the moment generating function of Y₁, find E[Y₁]. 1 - Q2(v.) Let Y₂ = X₁ – X2, and Mx, (t) = Mx₂ (t) = (1 t). Find the moment generating function of Y₂, and using the moment generating function of Y₂, find E[Y₂]. Q2(vi.) Using the bivariate transformation method, find the joint…Let Xbe a random variable with density function (2x² - 1Suppose that buses arrive are scheduled to arrive at a bus stop at noon but are always X minutes late, where X is an exponential random variable with probability density function fx(x) Ae-A. Suppose that you arrive at the bus stop precisely at noon. = (a) Compute the probability that you have to wait for more than five minutes for the bus to arrive. (b) Suppose that you have already waiting for 10 minutes. Compute the probability that you have to wait an additional five minutes or more.Let the probability density function of a random variable X be 630r (1 – 1)* if ()Find the characteristic function of X² when X has the N(u, o²) distribution.Consider the random variable X with PDF (known as Cauchy distri- bution) f(x) = 7 - 00Plz do fastI need help with this probability density function problem. It asks to calculate the probability that the battery lasts longer than 1 hour. Please show work so that I can understand future problems like this.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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