Intervals and decreasing on complement

Reference no: EM13983674

Derive formulas for the c.d.f. FY (y), and the p.d.f. fY (y), of a transformation Y = g(X) of a random quantity X, in terms of its c.d.f. FX(x), and p.d.f. fX(x), in the case when the trans- forming function y = g(x) is monotonically decreasing. Follow the line of reasoning used to derive the analogous formulas (3.1.11)-(3.1.12) for monotonically increasing transformations. How would you extend these formulas to transformations that are monotonically increasing on some intervals and decreasing on their complement?

Reference no: EM13983674

Questions Cloud

What is the final value of the speed of the gold nucleus : In this process work of 109.835 GeV is done on the gold nucleus. What is the final value of the speed of the gold nucleus as a fraction of c?

Autocorrelation function of the form : A zero-mean Gaussian random signal has the autocorrelation function of the form γX(τ) = 10e-0.1|τ| cos 2πτ. Write the covariance matrix for the signal sampled at four time instants separated by 0.5 seconds.

How far from the lens is the prism placed : The light passing through the prism is broken into its compent colors. If it is an equilateral prism (all of the prism angles are 60 degrees) made of crown glass (n=1.52) and the light is incident at a 30 degree angle to one face of the prism: How..

What is the global symmetry of the electroweak lagrangian : What is the global symmetry of the electroweak Lagrangian that gives rise to lepton number conservation? then perhaps it would not be easiest to give the global symmetry directly. This is perfectly fine of course.

Intervals and decreasing on complement : How would you extend these formulas to transformations that are monotonically increasing on some intervals and decreasing on their complement?

What is the density : We wish to determine the density of an unknown substance using only a spring scale and a beaker of water. in air sample has a weight of 28.4N. measures underwater it has a weight of 17.N. What is the density?

What is rate at which energy flows from the inside of house : What is the rate at which energy flows from the inside of the house to the outside through the window? If this same power were used to heat water at 100 oC and 1 atm., how much water would it boil in one minute?

Identify law at source of dispute in deweerth vs baldinger : Identify the law at the source of the dispute in DeWeerth v. Baldinger. Identify the district court's holding regarding the defendant's motion to dismiss in DeWeerth v. Baldinger

Did the entropy of the system increase or decrease : A glass of water is left sitting out in the kitchen. It contains 100g of ice and 400g of water. How much ice melts? Did the entropy of the system increase or decrease? How do you know?

User Account

All Pages