Question

Consider the following statements: 
(i) Environmental pollutant concentration is generally modeled using lognormal distribution. 
(ii) Environmental pollutant concentration is generally modeled using Poisson distribution. 
(iii) The weekly rate of exceedance of environmental pollutant concentration with regards to a given standard is generally modeled using lognormal distribution. 
(iv) The weekly rate of exceedance of environmental pollutant concentration with regards to a given standard is generally modeled using Poisson distribution. 
Choose the correct option(s) from the following:

• A. (i) and (iv) are correct.
• B. (i) is correct and (iii) is incorrect.
• C. (ii) and (iv) are correct.
• D. (ii) and (iv) are incorrect.

Hint:

- Lognormal distribution is used to model pollutant concentrations. - Poisson distribution is used for modeling rare events like exceedances.

Answer 1

The Correct Option is A, B

Step 1: Understanding the Distributions
- The lognormal distribution is commonly used to model environmental pollutant concentrations because these concentrations tend to be positively skewed, meaning they have a long tail to the right. This is typical for pollutants such as particulates in the air or contaminants in water.
The Poisson distribution is used to model rare events or occurrences over time, such as the exceedance of pollutant concentrations above a certain threshold. This distribution is appropriate for modeling the frequency of exceedances over a given period.
Step 2: Analyzing the Statements
Statement (i) is correct because environmental pollutant concentrations are indeed typically modeled using the lognormal distribution.
Statement (ii) is incorrect because the Poisson distribution is not typically used to model pollutant concentrations themselves, but it is used for rare events like exceedances.
Statement (iii) is incorrect because the weekly rate of exceedance is not modeled by the lognormal distribution, but rather by the Poisson distribution.
Statement (iv) is correct because the Poisson distribution is appropriate for modeling the rate of exceedance of pollutant concentrations.
Thus, the correct answers are (A) and (B).