Purchase Solution

Continuous Random Variables : Fubini's Theorem

Not what you're looking for?

Ask Custom Question

Show that if {see attachment} is a continuous random variable then ...

Please see attachment for complete list of questions.

Attachments
Purchase this Solution
Solution Summary

Fubini's theorem is used to prove an equality. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

Solution Preview

Please see the attached file for the complete solution.
Thanks for using BrainMass.

3. proof:

Proof. Assume that the probability density function is f(x). Since , we know that . Then by definition, we have
...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Solving quadratic inequalities

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

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Multiplying Complex Numbers

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

Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

View More Free Quizzes
Related BrainMass Solutions

  • Integration : Fubini's Theorem

    An integral is found using Fubini's theorem.

  • Verify Fubini's Theorem for an integral evaluated over an equilateral triangle.

    14044 Verify Fubini's Theorem for an integral evaluated over an equilateral triangle. Verify Fubini's Theorem for an integral evaluated over an equilateral triangle.

  • Fubini's Theorem

    14089 Verify Fubini's Theorem integral evaluated over equilateral triangle I am asked to verify Fubini's Theorem for an integral evaluated over an equilateral triangle.

  • Convergence in Probability

    Prove Theorem 9.2(d): If g is a real-valued function that is continuous at , then converges in probability to . b. Let Y1, Y2, ...Yn be independent random variables, each with probability density function for 0  y 1, 0 elsewhere.

  • Measure Theory and Dominated Convergence Theorem

    Dominated Convergence Theorem: Let X1, X2, ... be a sequence of random variables converging almost surely to a random variable X.

  • Find the double integral

    Provide a sketch and use fubini's theorem to determine the order of integration. 2. Determine the best order of integration to find the double integral ??

  • Statistics: bivariate normal distribution

    Provide a proof of the following theorem (see attached for full description): The Case of Normal Random Variables When the X 1- 's form a random sample from a normal distribution, f and T 0 are both normally distributed.

  • Statistics: Probability density function, central limit theorem

    Note that b) Central Limit Theorem (Lindberg Levy form): If are independent and identically distributed random variables with and for i =1,2,...n.

  • Property of continuous distributions

    As with discrete random variables, the probability distribution can be approximated by a smooth curve b. Probabilities for continuous variables can be approximated using discrete random variables c.

View More Related Solutions