aNSER:

If X and Y are independent RVs with pdf's e*, x20, and e, y 2 0, respectively, find the density functions of U = X and V=X+Y. Are U and V independent? %3D X + Y

Waiting for the Train. A commuter train arrives punctually at a station every half hour. Each morning, a commuter named John leaves his house and casually strolls to the train station. The time, in minutes, that John waits for the train is a variable with density curve y = 1/30 for 0< x< 30, and y = 0 otherwise. a. Graph the density curve of this variable.b. Show that the area under this density curve to the left of any number x between 0 and 30 equals x/30. What percentage of the time does John wait for the trainc. less than 5 minutes?d. between 10 and 15 minutes?e. at least 20 minutes?

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Let X and Y have the joint density function 1 f(x, y) x²y? x > 1, y > 1. Let U = XY and V = 3X/Y. (a) What is the joint density function of U,V? 1 fu,v(u, v) 2u?v (b) On what domain is this defined? u > 1 and

Let g(x, y) represent the density of gold deposits in units of kilograms per square kilometre near a windmill, where the coordinates a and y are measured in kilometres east and north of .1 .1 the windmill respectively. Which of the following must be equal to g(x, y) dæ dy? 0 1 :7J g(x, y) dz dy -1 1 .1 1 || g(2, y) da dy + I g(2, y) dæ dy -1 1 2 | g(x, y) dy dæ 0. O All of the above O None of the above

Let Y₁ and Y₂ have joint density f(y₁, y2) = 3c(1 - y₂) on 0 ≤ y ≤ 2 and 0 ≤ y₂ ≤ 1. What is the value of c? In question In question A: B:2 C: D:3 above, what is the value of P(Y₂ 1)? A: 0.55 B: 0.1 C: D 113

Find the mass and center of mass of the lamina that occupies the region D and has the given density function ?. D is bounded by y =    x , y = 0, and x = 1;  ?(x, y) = 9x

Let X and Y have the joint density function x ≥ 1, y ≥ 1. Let U = = 2XY and V = X/Y. (a) What is the joint density function of U,V? fu.v(u, v) = (b) On what domain is this defined? u > and ≤0< f(x, y) = 1 x²y²⁹