1) Since total probability is 1 so
2) The region is shown below
Hence the required probability is
Let X denote the diameter of an armored electric cable and Y denote the diameter of...
The diameter measurements of an armored electric cable, taken at n=25 points along the cable, gave a sample standard deviation s= 0.3 cm. Compute a 95% confidence interval for the variance of of diameter of these cables. Assume that the population distribution is normal. 0 (0.0593, 0.1560) O (0.0548, 0.1742) O (0.0531, 0.1478) O (-1.0465, 1.0465)
Let X and Y denote independent random variables with respective probability density functions, f(x) = 2x, 0<x<1 (zero otherwise), and g(y) = 3y2, 0<y<1 (zero otherwise). Let U = min(X,Y), and V = max(X,Y). Find the joint pdf of U and V.
Question 20 4 pt The diameter measurements of an armored electric cable, taken at n=25 points along the cable, gave a sample standard deviation s= 0.3 cm. Compute a 95% confidence interval for the variance o? of diameter of these cables. Assume that the population distribution is normal. 0 (0.0593, 0.1560) 0 (0.0548, 0.1742) O (-1.0465, 1.0465) (0.0531, 0.1478)
Let f(x,y)= K(x^2+y^2 ) in 0≤x≤1, 0≤y≤1. Determine the value of the constant K that makes f(x,y) a joint density function. (a) Find fx(x) (b) Find fy(y) (please answer (a) and (b))
3. Let X denote the temperature (°C) and let Y denote the time in minutes that it takes for the diesel engine on an automobile to get ready to start. Assume that the joint density for (X,Y) is given by fxy(x, y) = c(4x + 2y + 1),0 < x < 40,0 < y = 2 (a) Find the value of c that makes this joint density legitimate. (b) Find the probability that on a randomly selected day the air...
Let X and y denote the failure times of two components of an electrical system. suppose that two random variables X and Y have the joint density f(x,y)=4e^(-2x-2y) for x>0,y>0. Find the Marginal Density functions of Xand Y as well as covariance of X and Y
Show all work! Thank you! Sk(x+y) 0<x<1, 0<y</ 14. Determine k, so that fx.y(x, y)= otherwise is a joint pdf. 10 15. Determine k, so that fxy(x,y)= kry 0<x<1, 0<y<1. 6 otherwise is a joint pdf. k(xy?) 0<x<1, 0<y<1. is a joint pdf. Determine k, so that fx.x(x,y)= 1 otherwise 17. Determine k, so that fx.y(x,y)= kr 0<x<y<1 O otherwise is a joint pdf. k(x + y) 0<x< y<1 18. Determine k, so that fx. (x,y)= 1 0 otherwise is...
4. Let X and Y have joint probability density function ke 12-00o, 0< y< oo 0, otherwise where k is a constant. Calculate Cov(X, Y).
15. Let X and Y denote the lengths of life, in hundreds of hours, for co ponents of typesI and types II, respectively in an electronic system. The joint density of X and Y is given by Bre" (z +v)/2 f(z, y) = otherwise Find the probability that a component of type II will have a life lenght in excess of 200 hours. 16. Let the random variables X and Y have the joint p.d.f a. f(z,y)=ī, for (z,y) =...
Let f(x, y) = ( kxy + 1 2 if x, y ∈ [0, 1] 0 else denote the joint density of X and Y a) Find k b) Find the marginal density of X (because of the symmetry of the joint pdf, the marginal density of Y is analogous). c) Determine whether X and Y are independent. d) Find the mean of X e) Find the cumulative distribution function of X. Set up an equation (but no need to...