An article in Journal of Hydrology [“Use of a Lognormal

Chapter 4, Problem 180E

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

An article in Journal of Hydrology [“Use of a Lognormal Distribution Model for Estimating Soil Water Retention Curves from Particle-Size Distribution Data” (2006, Vol. 323(1), pp. 325–334)] considered a lognormal distribution model to estimate water retention curves for a range of soil textures. The particle-size distribution (in centimeters) was modeled as a lognormal random variable X with \(\theta=-3.8\) and \(\omega=0.7\). Determine the following:

(a) \(P(X<0.02)\)         (b) Value for x such that \(P(X \leq x)=0.95\)

(c) Mean and variance of X

Equation transcription:

Text transcription:

\theta=-3.8

\omega=0.7

P(X<0.02)

P(X \leq x)=0.95

Questions & Answers

QUESTION:

An article in Journal of Hydrology [“Use of a Lognormal Distribution Model for Estimating Soil Water Retention Curves from Particle-Size Distribution Data” (2006, Vol. 323(1), pp. 325–334)] considered a lognormal distribution model to estimate water retention curves for a range of soil textures. The particle-size distribution (in centimeters) was modeled as a lognormal random variable X with \(\theta=-3.8\) and \(\omega=0.7\). Determine the following:

(a) \(P(X<0.02)\)         (b) Value for x such that \(P(X \leq x)=0.95\)

(c) Mean and variance of X

Equation transcription:

Text transcription:

\theta=-3.8

\omega=0.7

P(X<0.02)

P(X \leq x)=0.95

ANSWER:

Solution:

Step 1 of 4:

The particle- size distribution (in centimeters) was modeled as a lognormal random X with = -3.8 and =0.7.

  1. We have to find P(X<0.02).
  2. We have to find the value for x such that P(Xx)=0.95.
  3. We have to find the mean and variance of X.


Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back