for clsewhere (a) Find the marginal density of X (b) Find the marginal density of Y (c) Find Var[X]
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![1. The joint density for the random variables (X, Y) is given below.
T22+39) for 0 < I< 1,0< yS1
S(1, y)
for clsewhere
(a) Find the marginal density of X
(b) Find the marginal density of Y
(c) Find Var[X]
(d) Find Var[Y]
(c) Are X and Y statistically independent?
(f) Find P(X > 1)
(g) If E[XY] = 0.5, find the correlation between X and Y
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- Find endpoint(s) on a N(0, 1) density with the given property. (a) The area to the left of the endpoint is about 0.14. Round your answer to two decimal places. Endpoint = i eTextbook and Media (b) The area to the right of the endpoint is about 0.76. Round your answer to two decimal places. Endpoint = i eTextbook and Media (c) The area between +z is about 0.90. Round your answer to two decimal places. Endpoint = ± i eTextbook and Media62Suppose that the joint distribution function of X and Y is given by f (x, y) =x+y If 0 < x < 1 and 0The joint probability density of X and Y is f(x, y). Find the marginal density of X at 0.4. The answer should be given to 2 decimal places. g(0.4) = f(x, y)= { 2(x + y) 0A pdf is defined by : f (x, y) = [ C (x + ay) if 0Find (,) for the lamina of uniform density p bounded by the graphs of the equations x = 169-y² and x = 0. 0 (7,5) = (0, 338) O 5 O (7.5)=(338.0) y) 0 (7.5)=(0.676) O y) 26 0 (F.J) = (2.0) O 0 (57.5J) = (676,0) O (x,y)"Medians, etc problem." Suppose X has density x−2 for x ≥ 1. Find the density function for Y = X2.1.) Suppose X and Y have joint density function f(x,y)= 8xy/3 on x is greater than or equal to 0 and less than or equal to 1. and y is greater than x and is less than or equal to 2x. a.) Find P( Y< 0.8) b.) Find the marginal density function of X c.) What is E(X)?The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A = 25 and B = 35. (a) Determine the pdf of X. f(x) = Sketch the corresponding density curve. f(x) 0.20 0.15 0.10 0.05 O f(x) 0.20 0.15 0.10 0 0.05 25 25 30 30 SXS otherwise 35 35 (b) What is the probability that preparation time exceeds 26 min? f(x) 0.20 O 0.15 0.10 0.05 f(x) 0.20 0.15 0.10 0.05 25 25 30 30 35 35Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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