Purchase Solution

Proof of density function

Not what you're looking for?

Ask Custom Question

In the game of odd man wins, three people toss coins. The game continues until someone has an outcome different from the other two. The individual with the different outcome wins. Let X equal the number of games needed before a decision is reached. Prove by induction that the density function of X is (see attached).

Attachments
Purchase this Solution
Solution Summary

This is a probability proof by induction regarding density function. The induction that the density function is reached is determined.

Solution Preview

Proof:

Suppose T is tail, H is head. For one game, there are 8 outcomes:
TTT, HHH, TTH, THT, HTT, HHT, HTH, THH
Two of ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

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

Probability Quiz

Some questions on probability

Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

Graphs and Functions

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

Solving quadratic inequalities

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

View More Free Quizzes
Related BrainMass Solutions

  • Integrate an Inequality and Find a Density Function

    -(y^2)/2 < (1 + y^-2)e^-(y^2)/2 and also calculates the density function of log functions.

  • Probability density function

    205583 Probability density function proof See file. thanks Show that the function...defines a PDF of some random variable. see attached This provides an example of working with a proof regarding a probability density function.

  • Probability: continous random variable

    Then the distributive function of is Then the probability density function of is Therefore, we have Using brief, step by step calculations in an attached Word document, this solution proves the probability density function.

  • Stochastic Differential Equations, Density Functions and Random Variables

    (Hint: you will need to know how to find the density function for X ? μ from the density function for X). (b) If ...., and X1 and X2 are independent, prove that .....

  • Continuous Random Variables : Fubini's Theorem

    Please see attachment for complete list of questions. 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 .

  • Convergence in Probability

    solution contains the proof of the theorem "If g is a real-valued function that is continuous at a, then g(a^) converges in probability to g(a)" and an application of this theorem for a continuous random variable.

  • Jointly Distributed Random Variables : Gamma and Exponential Distributions

    A random variable is said to have a gamma distribution with parameters if its density function is where A random variable is said to have an exponential distribution with parameters if its density function is

  • Random Variables

    Since X follows Chi-squared distribution with degree of freedom v, we know its density function is given by (*) ,by (2).

  • Solutions, Density, Molecular weight

    Calculate the number of grams of alcohol present in 1.00 L of 51 proof gin. The density of ethanol is 0.798 g/mol. (solution in grams, please) Arginine vasopressin is a pituitary hormone.

View More Related Solutions