Question

The probability of encountering different concentrations of pollutant X in a water supply [in arbitrary units]...

The probability of encountering different concentrations of pollutant X in a water supply [in arbitrary units] is described by an exponential distribution with parameter λ=0.5.

a) Calculate and plot the CDF FX(x) for the concentration of pollutant. 


b) Use the CDF to calculate the probability the concentration of X is higher than 4 [same arbitrary units]. 


c) Use the CDF to calculate the probability the concentration of X is less than 4 but higher than 2 [same arbitrary units] 


d) The probability of developing a disease D is 0.07, 0.2, and 0.33 for people exposed to X concentrations < 2, between 2 and 4, and over 4 respectively. What is the probability a person consuming this water develops the disease? 


Math   Statistics-And-Probability   
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Homework Answers

Answer #1

a)

The pdf of X is

The CDF of X is

Following is the plot of CDF:

(b)

(c)

d)

From given information we have

By the law of total probability, the probability a person consuming this water develops the disease is

Answer: 0.1354

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