5. Let X and Y be jointly continuous with joint density function 0≤x≤ y ≤ 2 otherwise. (b) [(x+y), 10, Find the marginal density function fy (y) of Y; f(x, y): = Calculate the probability P(Y < 2X).
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- The time T a business is closed after a fire has the cumulative distribution function (부)- 3 1 1 F7(t) = t>0 t+1 otherwise = VT. The cost to the insurer is X = Determine the density of X for x > 0.The joint density function of Y1 and Y2 is given byf(y1, y2) = (y1 + y2, 0 < y1 < 1, 0 < y2 < 1,0, elsewherea) Find marginal density functions. Are Y1 and Y2 independent?b) Could you tell whether Y1 and Y2 were independent or not without finding marginaldensity functions? Explain.c) Find P(Y1 + Y2 < 0.2).d) Find P(0 < Y2 < 0.5|Y1 = 0.4).The lifetime of a machine part has a continuous distribution on the interval (0,45) months with probability density function f, where f(x) is proportional to (4+x)-2. Find the probability that the lifetime of the machine part is less than 7 months.
- 6. Determine the value of c that makes the function f(x,y) = cxy a joint probability %3D density function over the range 0Let X have the uniform distribution on the interval [1, 3]. Find the density function of Y =X^2.Let the joint probability density function of (X, Y) be fx,y (x, y) = Cx-¹(y-x)³-¹, 00,ß > 0. Show Transcribed Text (f) Find Pr(X + Y ≤ } }); (j) Find Pr(X> 31).The joint density function of X and Y is given by f(x, y) = 2x + 2y,0< x< y <1. | Find the marginal densities fx (x) and fy (y). | Write the density function of the random variable X + Y. Verify that E(X+ Y) = E(X)+ E(Y) using your distributions from parts (a) and (b).For the probability density function f(x) = 3x^2 on [0,1], find: V(X)Suppose X,Y have joint density function f(x,y) = (12/7)(xy+y^2), 0 <= x <= 1 and 0 <= y <= 1 and 0, otherwise. a) Check that f is a genuine joint density function. b) Find the marginal density functions of X and Y. c) Calculate the probability P(X < Y).Let X and Y has joint probability density function * y? A(X, Y) 81 ,0For x1, the marginal distribution fx1 (x1) function is validis it a density function)Let (X, Y)' be a random vector with the following density function: (8xy if0sxsysl elsewhere Find the marginal density functions of X and Y. Are X and Y independent? f(x)=SEE MORE QUESTIONSRecommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON