Solution Found!
An article in Journal of Hydrology [“Use of a Lognormal
Chapter 4, Problem 180E(choose chapter or problem)
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.
- We have to find P(X<0.02).
- We have to find the value for x such that P(Xx)=0.95.
- We have to find the mean and variance of X.