If X is exponential with rate , find P{[X] = n,X [X] x}, where [x]

Question:

If X is exponential with rate λ, find P{[X] = n,X − [X] ≤ x}, where [x] is defined as the largest integer less than or equal to x. Can you conclude that [X] and X − [X] are independent?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

A First Course In Probability

ISBN: 9789332519077

9th Edition

Authors: Sheldon Ross

See More Books

Question Posted: Oct 22, 2015 02:59 AM

See More Questions

If U is uniform on (0, 2) and Z, independent of U, is exponential with rate 1, show directly (without using the results of Example 7b) that X and Y defined by X = 2ZcosU Y = 2ZsinU are independent...
If both A' and Y, distributed independently, follow exponential distributions with mean parameter 1. Find the distributions of (a) U = X + Y, and (b) V = X/(X + Y).
X is an exponential random variable with = .3. Find the following probabilities. a. P(X > 2) b. P(X < 4) c. P(1 < X < 2) d. P(X = 3)
Ethanol reacts with sodium and forms two products which are Options: 1) Sodium ethanoate and hydrogen 2) Sodium ethanoate and oxygen 3) Sodium ethoxide and hydrogen 4) Sodium ethoxide and oxygen
The average farm in the United States in 2004 contained 443 acres. The standard deviation is 42 acres. Use Chebyshevs theorem to find the minimum percentage of data values that will fall in the range...
Lagman Corporation purchased land for $310,000. Later in the year, the company sold a different piece of land with a book value of $114,000 for $81,000. How are the effects of these transactions...
A parallel-plate capacitor connected to a battery maintaining a potential difference $V$ across the capacitor initially stores electric potential energy $U_{1}^{E}$. If the plate area is doubled...
Knife Edge Company purchased tool sharpening equipment on July 1, 2010, for $16,200. The equipment was expected to have a useful life of three years and a residual value of $900. Instruction...
All work must be shown on every facet of the solution. This includes a timeline with cashflows, timing and rates clearly laid out and formulas (in pure form, not in the calculator or excel form). A...
a. What are the prospects for a PE that overleverages due to cheap funding sources? b. What are the pros and cons of becoming a public company? c. Suppose that Lululemon raises $2 million in series A...
A rectangular array of mn numbers arranged in n rows, each consisting of m columns, is said to contain a saddlepoint if there is a number that is both the minimum of its row and the maximum of its...
Suppose that F(x) is a cumulative distribution function. Show that (a) Fn(x) and (b) 1 [1 F(x)]n are also cumulative distribution functions when n is a positive integer. Let X1, . . . ,Xn be...
Which neoclassical argument claims that money and interest rates react in a certain way to outside shocks so as to lead back to equilibrium?
The skin friction coefficient of a laminar boundary layer developing over a flat plate is measured as 0.00347, a certain distance downstream of the leading edge of the plate. The working fluid is air...
A horizontal cantilever beam (length 3L) is fixed at the wall at the left end and vertically constrained at the right end. There is a hinge located at x = L and a point load, P, at x = 2L acting...
2. a) A heat pump designed to deliver heat at 55C absorbs heat from low temperature environment at 5*C. CoP of the heat pump is 5. Calculate CoP of an equivalent Carnot heat pump and discuss how the...
Q1) The shape given in the figure below is located on Frame A with an offset of 2m on ya-axis and the circle M is located on the middle of the surface of the shape. Zc X Yc+ C Za 5m A Xc Va 2m 1m Xb...
dynamics a Write the first law of thermody in differential form Q = du +dw by calculating du and the work tw for a photon gas, (Do not over think otw !)
In Problems 5378, find an equation for the line with the given properties. Express your answer using either the general form or the slope-intercept form of the equation of a line, whichever you...
From a medical tourist perspective, compare Shouldice with the traditional hospital in terms of the key factors of competition. Using Table 15-3, why would Shouldice attract patients from outside the...
Indicate which of the following random variables are discrete and which are continuous. a. The amount of rainfall in a city during a specific month b. The number of students on a waitlist to register...
Let x be the number of potential weapons detected by a metal detector at an airport on a given day. The following table lists the probability distribution of x. Calculate the mean and standard...
Refer to Exercise 5.14. Calculate the mean and standard deviation for the probability distribution you developed for the number of defective tires on all 1300 H2 Hummer limousines. Give a brief...
Can you explain key factors that will contribute to the success or failure of a business plan based on: product differentiation branding and marketing distribution and availability effective supply...
The idea that teens seem to share many similar behaviors is an example of: a. Generational microculture b. Age-based microculture c. Gender microculture d. Social class microculture
Topic of this Week's discussion is... Entry Strategies and Strategic Alliances Global Marketing and R&D The opening case explores the development of blockchain technology and how it has the...

If X is exponential with rate , find P{[X] = n,X [X] x}, where [x]

Question:

Step by Step Answer:

For 0 x 1 PX n X X x Pn X n x e n e n x e n 1 e x Becau...View the full answer

A First Course In Probability

Students also viewed these Statistics questions