Purchase Solution

Molecule Speed

Not what you're looking for?

Ask Custom Question

This is for question #3 on the attached page...

You will need the following fact for Question #3.

integral_{-infinity}^{+infinity} e^(-x^2/2 sigma^2) dx / sqrt(2*pi*sigma^2) = 1

This is in Section 5.4: it just says that the function

e^(-x^2/2 sigma^2) / sqrt(2*pi*sigma^2)

is a density (it is the "famous" normal density with mean 0 and variance sigma^2).

By using symmetry about 0 and the above fact, you can finish Question #3 with one integration by parts.

Purchase this Solution

Solution Summary

The solution discusses (Ross # 5.1 - Theoretical) The speed of a molecule in a uniform gas at equilibrium is a random variable whose probability density function is given by ....

Solution Preview

Solution for question #3 only.

integral (-inf to inf) [e^(-x^2/2 sigma^2) dx / sqrt(2*pi*sigma^2)] = 1
=> integral (-inf to inf) [e^(-x^2/2 sigma^2) dx] = sqrt(2*pi*sigma^2)
=>integral (0 to inf) [e^(-x^2/2 sigma^2) dx] = sqrt(2*pi*sigma^2)/2
=> integral (0 to inf) [e^(-c*x^2) dx] = sqrt(pi/c)/2

Because, probability function,
f(x) ...

Solution provided by:
  • BEng, Allahabad University, India
  • MSc , Pune University, India
  • PhD (IP), Pune University, India
Recent Feedback
  • " In question 2, you incorrectly add in the $3.00 dividend that was just paid to determine the value of the stock price using the dividend discount model. In question 4 response, it should have also been recognized that dividend discount models are not useful if any of the parameters used in the model are inaccurate. "
  • "feedback: fail to recognize the operating cash flow will not begin until the end of year 3."
  • "Answer was correct"
  • "Great thanks"
  • "Perfect solution..thank you"
Purchase this Solution

Free BrainMass Quizzes
Know Your Statistical Concepts

Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.

Measures of Central Tendency

Tests knowledge of the three main measures of central tendency, including some simple calculation questions.

Measures of Central Tendency

This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.

Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.