. Jan wins, ue OTCS LICO. 6.127 Consider two identical electrical components. Let X and Y denote the respective lifetim...
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
Wiout feplacement. 6.9 Consider a sequence of Bernoulli trials with success probability p. Let X denote the number of trials up to and including the first success and let Y denote the number of trials up to and including the second success. a) Identify the (marginal) PMF of X c) Determine the joint PMF of X and Y. d) Use Proposition 6.2 on page 263 and the result of part (c) to obtain the marginal PMFS of X and Y....
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.
ciule jolh! PMF and the marginal PMFs? 6.14 Let X and Y be discrete random variables. Show that the function p: R2 R defined by p(r, y) px(x)pr(y) is a joint PMF by verifying that it satisfies properties (a)-(c) of Proposition 6.1 on page 262. Hint: A subset of a countable set is countable CHAPTER SIX Joindy Discrete Random Variables 6.2 Joint and marginal PMFs of the discrete random variables x numher of bedrooms and momber of bwthrooms of a...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse (both in years). Assume the joint probability density function of X and Y is f(x,y) = (x? + 2 + 2) 0<x< 1, 0 < y < 2 a. What is the probability that both fuses last at most 4 months? b. What is the probability that the first fuse lasts less than...
There are two fuses in an electrical device. Let X denote the lifetime of the first fuse, and let y denote the lifetime of the second fuse both in years). Assume the joint probability density function of X and Yis f(x,y) – $(x +2y). 0<x<1, 0 <y<2 a. What is the probability that both uses last longer than 4 months? b. What is the probability that the second fuse lasts less than 3 months given that the first fuse last...
Suppose that the two components operate independently and have identical performance characteristics. Let X and Y be random variables denoting their life spans. Experience with wear-out times suggests that in certain cases a good choice for fx,y(x, y) would be fxx (x, y) = {?? 122e-1(x+y), x > 0,y>0 otherwise Where 2 is some constant greater than 0. Suppose that the manufacturer advertises a money-back guarantee if the system fails to last for more than 1000 hours. a) What proportion...
Q6. The lifetimes of two components in a machine have the following joint pdf: f(x, y).00-x y) for 0<50-y < 50 and zero elsewhere a. What is the probability that both components are functioning 20 months from now. b. What is the probability the component with life time X would fail 3 months before the other one? c. Compute the covariance of X, Y d. Compute the expected life of the machine e. What is probability that the two components...
3. Let f(x,y) = xy-1 be the joint pmf/ pdf of two random variables X (discrete) and Y (continuous), for x = 1, 2, 3, 4 and 0 <y < 2. (a) Determine the marginal pmf of X. (b) Determine the marginal pdf of Y. (c) Compute P(X<2 and Y < 1). (d) Explain why X and Y are dependent without computing Cou(X,Y).
Consider 3 jointly discrete andom variables X, Y, Z whose joint PMF is given by p(x, y, z) = {((x+ + xz? + yz), x = 1,2, y = 2,3, z = 0,1 0, otherwise a) Find the constant c. b) Find Pxy(x, y) c) Find E[xy?) Remaining Time: 11 minutes, 31 seconds. Question Completion Status P.2 (30 points) (10 Points) Use VCO block, build a Simulink model to simulate FM transmitter with the following parameters - Message signal 0.5sin(10000mt)+2sin(6000m+30°)...