Show that if the exponentially decreasing functionif x < 0if x > 0f(x) = LAeis a probability density function, then A = c.

Given: fx=0 ; if x<0Ae-cx ; if x≥0 For a probability density function f(x).…

Answered: Show that if the exponentially…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Random variable T has the following Weibull probability density function (PDF):
Find a value of k that will make fa probability density function on the indicated interval. f(x) = kx, [1, 4] k = (Type an integer or a simplified fraction.)
At a restaurant, the density function for the time a customer has to wait before being seated is given by f(t) = 2e¯ if t > 0. Find the probability that a customer will have to wait at least 6 minutes for a table. Probability = .000006 -2t
For what value of c is the function f(x) = {c/x³ if x ≥ 1 {gx3 otherwise a probability density function?
сх, f(x)= 0
The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…
Let X be a random variable with the probability density function f(x) = { ae; x>0 0 ; otherwise Find (i) Value of a
Consider a constant function: f(x)= c; a ≤ x ≤ b Suppose that the function represents a probability density function and c<1 , which of the following is true? a. |a−b|<0 b. |a−b|<1 c. |a−b|>1 d. |a−b|=1
Find the value of k that makes the given function a probability density function on the specified interval. f(x) = kx 2 ≤ x ≤ 6 k= || =
Verify Property 2 of the definition of a probability density function over the given interval. 1 10 f(x)= [4,6]

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Show that if the exponentially decreasing function if x < 0 if x > 0 f(x) = LAe is a probability density function, then A = c.