Purchase Solution

# Probability: Random Variable and Probability Density Function

Not what you're looking for?

Problem 1: A random variable X takes values between 0 and infinity with a probability density function
f(x) = A + Be^(-x) for 0 <= x <= infinity.
a) find A and B
b) find expected value of X
c) what is the median of X?

##### Solution Summary

The expected value and median of a random variable are found. The full calculations are shown.

##### Solution Preview

a.)
because,
integration(0 to infinity)[f(x) dx] = 1 (total probability = 1)
=>integration(0 to infinity)[(A+B*exp(-x)) dx] = 1
=> A*x - B*exp(-x)|(0 to infinity) = 1
=> A = 0 ( because x value is from 0 to infinity, because of ...

Solution provided by:
###### Education
• 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."
• "Great thanks"
• "Perfect solution..thank you"

##### Free BrainMass Quizzes

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.