Answered: A continuous variable X has a…

A continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4, and p(x)=0 otherwise. What is the value of the normalisation constant, A

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

Related questions

Q: Show that the probability density function of a negative binomial random variable equals the…

A: Given that Show that the probability density function of a negative binomial random variable equals…

Q: Consider a tandom variable X with the following probability density function f(x) = a,x > 2 which is…

Q: Suppose a continuous random variable X has the probability density function f(a) 2e-2,r 2 0. Compute…

Q: 2. Suppose that the random variable X possess a uniform distribution on the interval (0, 1). Let…

Q: Let X be a random variable with probability density function f(x) = c(8x-x^2) if 0<x<8 otherwise…

A: Given: x is a random variable with probability density function. f(x)=c(8x-x2) if0<x<80…

Q: Determine the value of c for which the function below will be a probability density functi So(8x' -…

A: Here given thatf(x)=c8x3-x4 ; 0≤x≤80 ; other

Q: Please solve all correctly and asap

Q: Suppose X = 1/(1+Y), where 12 Y ~ fy(y) = y > 0, %3D 0, Identify the distribution of X by name and…

A: It is an important part of statistics . It is widely used .

Q: The function f(x) is the probability density function, that describes the random variable travel…

Q: let x denotes the percentage of time out of 40 hour workweek that a call center agent is serving a…

Q: True or False The Poisson probability density P(x), when evaluated at x equal to its mean value, is…

Q: If the lifetime for a type of lamps follows a distribution with density function f(x)…

A: Given f(x)=12x2(1-x) 0≤x≤1 Where x in year P(x<7.5 months)=?

Q: The length of time X (measured in days) that a gadget lasts has the following probability density…

A: Here Given p.d.f for the lifetime of gadget

Q: The density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).

A: Given:fx=cx2, x≥10…

Q: Give an example of a probability density function fx(x) whose associated continuous random variable…

A: Here, need to give an example of a probability density function fX(x) whose associated continuous…

Q: fx1,x₂(x1, x₂) = 0, otherwise. What is the joint probability density function fy₁,Y₂ of Y₁ = X₁/X2…

Q: The Boris and Bela Pharmacy have determined that the shelf life of B5 Nutrient is a Continuous…

A: Sample space, S

Q: A random variable X has a cumulative distribution function given by x≤5 F(x)=- x>5 Find the…

A: Hi! Thank you for the question. As per the honor code, we are allowed to answer 1 question at a…

Q: A continuous random variable X has a normal distribution with mean 6. The probability that X takes a…

A: Given information Mean (µ) = 6 P(X > 15) = 0.38 P(Z > z) = 0.38 P(Z < z) = 1 – P(Z>Z) =…

Q: Consider the probability density function f ( x ) = kxe^3x 1≤x≤2 = 0…

A: Given information: It was stated that the pdf of x is given as, f(x)=k x e3x ; 1≤x≤20 ; O.w…

Q: Let X₁, X₂ be IID with \Exp(1), the standard exponential distribution. Show that Z = X₁/X₂ has an…

A: Let X1 , X2 be the iid random variable having exp(1) Then show that Z=X1/X2 has F distribution…

Q: A random variable X follows the continuous uniform distribution with a lower bound of - 4 and an…

A: Answer: From the given data, X~Uniform distribution Lower bound of -4 and Upper bound of 12

Q: The life lengths of two transistors in an electronic circuit is a random vector (X; Y ) where X is…

A: Solution

Q: Let X be the lifetime (measured in hours) of an electronic device. suppose that X let X be a…

Q: A continuous variable Y has a probability density function for which the moment generating function…

Q: If a continuous RVX (> 0) possesses memoryless property, that is P(X>x+h)= P(X > x). P(X > h), then…

Q: A continuous random variable X has a normal distribution with mean 62. The probability that X takes…

A: µ = 62. P(X > 65.8) = 0.12

Q: 0, x < 0 Find the probability that a telephone call selected will last beyond 5 minutes.

Q: Let X be the arrival time in minutes of the next red traffic light on a certain delivery route. We…

Q: The probability density function for the continuous random variable X is given by: (A(x² – 2x + 21)…

A: Farmula used. V(X)=E(X2)-[E(X)]2 Sd(X)=√Var(X)

Q: The conditional expectation of X given Y=y is the sum or the integral of the marginal probability…

Q: The median of the random variable X whose probability density function 3. f(y) = }2 x² ,0 < x < 2 4…

Q: What is the expected value of a continuous probability distribution given by the density function…

A: Given that,The density function is

Q: 11. Let Y be a random variable with density function cye-2y if 0≤ y <∞, elsewhere. 0 f(y) = {cu (a)…

A: "As per the Bartleby guidelines, we can solve only one question at a time.Therefore, we are solving…

Q: A random variable X has probability density function for 0 < x < 2, 4 f(x) = { +(2x –- 3) for 2 < x…

A: Given:

Q: 2- Let the probability density function of the random variable X is = {²()* 0 f(x) = ,x= 1,2,3,... ,…

A: Given information:

Question

100%

A continuous variable X has a probability density function given by p(x)=Ax^2 for 0≤x≤4, and p(x)=0 otherwise.

What is the value of the normalisation constant, A?

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Suppose that a positive continuous random variable X has probability density function given by f(x)=c(14-5x^2), where c is a constant. What is the variance of this random variable? TYPE YOUR ANSWER AS THE NEAREST NUMBER WITH TWO DECIMAL DIGITS.
Show that the standard normal probability density function f(x) has points of inflection when x = ±1.
g) What is the standard deviation of X? h) What is the probability that X is more than 2 standard deviations above its expected value? i) What is the expected value of X4?
What is the expected value of a continuous random variable X with probability density function (pdf) given by f(x) = 2x, 0 < x < 1?
Please help
If X = ln Y has a normal distribution with the mean μand the standard deviation σ, find the probability densityof Y which is said to have the log-normal distribution.
The "kernel trick" is a quick way to integrate when you can recognize a distribution in some equation g(x) which you want to integrate. It takes advantage of the fact that the pdf f(x) of a proper probability distribution must integrate to 1 over the support. Thus if we can manipulate an equation g(x) into the pdf of a known distribution and some multiplying constant c in other words, g(x) = c · f(x) --- then we know that C • --- Saex 9(x)dx = c Smex f(x)dx = c ·1 = c Steps: 1. manipulate equation so that you can recognize the kernel of a distribution (the terms involving x); 2. use the distribution to figure out the normalizing constant; 3. multiply and divide by the distribution's normalizing constant, and rearrange so that inside the integral is the pdf of the new distribution, and outside are the constant terms 4. integrate over the support. The following questions will be much easier if you use the kernel trick, so this question is intended to give you basic practice. QUESTION:…
Let X be a continuous random variable with range [−ln5,0] and its probability density function is given by the following function: f(x)=ce^−x, where cc is a constant. (1) Find the value of c . Answer: (2) Find the probability P(−ln2≤X≤0) . Answer:
The diameter of a particle of contamination (in micrometers) is modeled with the probability density function 2 f(x)= = x3 for x > 1 . What is the probability that the diameter of the particle of contamination is below 2 micrometers?
the probability density function for the waiting time was given by f(x) = 0 for x 15 a) Find the expected value of the waiting time, X minutes. b) Find the variance and standard deviation of the waiting time. c) What is the probability that the waiting time is within two standard devia- tions of its expected mean value? 1 15
The waiting line at a popular bakery shop can be quite long. Suppose that the waiting time in minutes has probability density function f(x) = 0.2 · e-0:2-* Calculate the mean and variance for the random variable: E(X) = i V(X) = i