If a random variable has the gamma distribution with α=2 and β=3, find the mean and the standard

Name: Problem 52, Chapter 5: Probability and Statistics for Engineers
Uploaded: 2023-11-23T16:54:57-08:00
Duration: 1 min 9 s
Channel: Prabhakar Kumar
Description: If a random variable has the gamma distribution with α=2 and β=3, find the mean and the standard deviation of this distribution.

step 1 In this question, we have been given to calculate the value of mean and standard deviation of ga

Question

If a random variable has the gamma distribution with $\alpha=2$ and $\beta=3$, find the mean and the standard deviation of this distribution.

   If a random variable has the gamma distribution with $\alpha=2$ and $\beta=3$, find the mean and the standard deviation of this distribution.

Probability and Statistics for Engineers

Miller & Freund 9th Edition

Chapter 5, Problem 52

Instant Answer

Solved by Expert Prabhakar Kumar

11/23/2023

Step 1

The mean of a gamma distribution is given by: Mean = α * β The variance of a gamma distribution is given by: Variance = α * β^2 The standard deviation is the square root of the variance: Standard Deviation = √(Variance) Show more…

Show all steps

Thanks for your feedback!

If a random variable has the gamma distribution with $\alpha=2$ and $\beta=3$, find the mean and the standard deviation of this distribution.

Play audio

Feedback

Prabhakar Kumar and 97 other educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Gamma Distribution

The gamma distribution is a two-parameter family of continuous probability distributions characterized by a shape parameter and a scale parameter. It is frequently used to model waiting times and processes with a skewed distribution, such as rainfall amounts or the time until a specified number of events occur. Its properties make it particularly useful in areas like reliability analysis and queuing theory.

Mean and Variance in Gamma Distribution

For a gamma-distributed random variable, the mean (expected value) is calculated as the product of the shape parameter and the scale parameter, while the variance is the product of the shape parameter and the square of the scale parameter. These formulas provide a straightforward way to compute the standard deviation, which is the square root of the variance, indicating the spread of the distribution around its mean.

Please give Ace some feedback