Purchase Solution

Probability : Density of the Sum of Independent Variables

Not what you're looking for?

Ask Custom Question

We have found the density of the sum of two independent U(0,1) variables. Use that result to find the density of the sum of three independent U(0,1) variables.

(You will need to treat intervals (0,1), (1,2) and (2,3) separately, although an appeal to symmetry can reduce the work. Give yourself a gold star if you get the right answer first go - get the limits of the integrals correct).

See the attached file for the problem.

Attachments
Purchase this Solution
Solution Summary

The density of the sum of independent variables are discussed. The solution is detailed and well presented.

Purchase this Solution
Free BrainMass Quizzes
Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

View More Free Quizzes
Related BrainMass Solutions

  • Statistics: Probability density function, central limit theorem

    Differentiating we get By the transformation of random variables the probability density function of Y is given by Thus This is the probability density function of lognormal distribution.

  • Distribution Theory

    The solution describes the determination of the joint distribution of the sum of n independent Exponential random variables.

  • Probability density function

    Find (a) c (b) Pr {min (X, Y) 1/3} (c) Pr {X <= Y} (d) The marginal probability density function of X (e) E [XY] 5) Let X and Y be independent uniform (0,1) random variables.

  • Gaussian Random Variables

    The sum of a random number of independent Gaussian random variables with zero mean and unit variance results in a Gaussian random variable regardless of the distribution of N (the number of variables in the sum). keywords: rv, r.v.

  • Random Variables

    The marginal density of Y1 is and the marginal density of Y2 is Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2.

  • Random Variable

    37) Let X1, X2, ...., Xn be independent random variables, each having a uniform distribution function of M, Fm (.), is given by Fm(x)=x^n, 0(less than or equal to)x(less than or equal to) 1 What is the probability density function of M?

  • Marginal Probability Density Function and Expected Values

    b) Find the marginal probability density function for each of the random variables. Are the weekly profits of these two stores independent? (c) Calculate the probability that in one particular week, the profit of store B will be less than $2000.

  • Probability Problems

    For independent variables correlation is zero Calculation of covariance, marginal probability, expectation, probability density function, log normal distribution. The answers are given with interpretation of results.

  • Characteristics of Normal Distribution

    The graph of the associated probability density function is bell-shaped, with a peak at the mean, and is known as the Gaussian function or bell curve. Characteristics of Normal Distribution 1.

View More Related Solutions