Statistics Probability 28059
Exponential random variable
This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

I)Let X be an exponential random variable with mean 1,and Y = exp^(X/2):
a)find F(y)
b)Evaluate E(Y)
c)Evaluate E[(Y^2)/(1+(X^2))]
II)The random variable X is uniformly distributed on the interval [1,3].Find the probability density function fy(y)of the random variable Y=2X+5

Â© BrainMass Inc. brainmass.com May 24, 2023, 1:36 pm ad1c9bdddf https://brainmass.com/statistics/probability/exponential-random-variable-28059
This shows how to find the probability density function.

$2.49

Add Solution to Cart
Remove from Cart

ADVERTISEMENT

$2.49

Add to Cart
Remove from Cart

How the Solution Library Works
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!"

ADVERTISEMENT
Free BrainMass Quizzes
Terms and Definitions for Statistics

This quiz covers basic terms and definitions of statistics.

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.

Measures of Central Tendency

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

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.

View More Free Quizzes

Related BrainMass Content
View More

ADVERTISEMENT