Problem regarding the random division

Reference no: EM13983804

1. Let f .x/ be the uniform density on Œ0; 1] and let g.x/ be the density on Œ0; 1] given by g.x/ Dcex , where c is the normalizing constant.

Let F; and G be the corresponding CDFs. Find the density function correspond- ing to the new CDF H.x/ D F.x/G.x/.

2. * (Random Division). Jen's dog broke off her six-inch-long pencil at a random point on the pencil. Find the density function and the expected value of the ratio of the lengths of the shorter piece and the longer piece of the pencil.

3. (Square of a PDF Need Not Be a PDF). Give an example of a density function f .x/ on Œ0; 1]such that cf 2.x/ cannot be a density function for any c.

4. (Square Root of a PDF Need Not Be a PDF). Give an example of a density function f .x/such that cpf .x/ cannot be a density function for any c.

Reference no: EM13983804

Questions Cloud

The variance and standard deviation of n-1 : Need calculations and answers for the following using the variance and standard deviation of N-1 in the denominator 5,6,2,8,7,6,6,12,6,5,4,5

Coupons are paid semi-annually : Coupons are paid semi-annually. Determine the spot rate for the 1.5-year period, expressed as a nominal rate compounded semi-annually.

Will the mirror be concave or convex : You want to create a spherical mirror with a focal length of +15.0 cm. Will the mirror be concave or convex?

Find the probability mass function of x : Please answer the following questions for an assignment!!! 1) A fair (unbiased) die is thrown. Let X be the number shown up. (a) Find P (|X - E(X)| ≥ 2.5).

Problem regarding the random division : Jen's dog broke off her six-inch-long pencil at a random point on the pencil. Find the density function and the expected value of the ratio of the lengths of the shorter piece and the longer piece of the pencil.

Calculate the magnitude of the angular momentum l : Develop an expression for the velocity vector v(t) in m/s) of the coconut as a function of the given information, the free-fall time t, and variables available in the palette. Let t = 0 be the moment that the coconut is released. Express your answ..

Calculate the phase constant for the harmonic oscillator : Calculate the phase constant Φ (in radians) for the harmonic oscillator with the velocity function v(t) given in the figure.

Calculate probability with replacement : How do I calculate probability with replacement? for ex the formula

Example of a density function : 1. * Give an example of a density function on Œ0; 1] by giving a formula such that the density is finite at zero, unbounded at one, has a unique minimum in the open interval .0; 1/, and such that the median is .5.

User Account

All Pages