4.66 The annual rainfall in inches in a certain region has a normal distribution

Question

4.66 The annual rainfall in inches in a certain region has a normal distribution with a mean of 40 and variance of 16. What is the probability that the rain fall in a given year is between 30 and 48 inches? Additionally, this Matlab problem: In Matlab, using the randn() function. generate a large number (N > 10000) of values of the random variable from problem 4.66. 1) Using the relative frequency definition of probability, compute the probability that the rainfall is between 30 and 48 in. 2) Using the definition of expected value as arithmetic mean of a very large number of values of the random variable. compute the expected value. Note: None of 1) or 2) require using the PDF or CDF or computing an integral. Once you have the N values, you can forget that they come from a normal distribution.

Explanation / Answer

in the given problem :

u require to generate random number with mean 40 and variance 16.. paste this to do so :

population = 40 + (1/4)* randn(1,10000) ;

this will generate 10,000 sample of gaussian distribution with mean 40 and variance 16.

a. next job is to find the total count of number between 30 & 48 in those samples . we have to set up a loop to do so.. do this :

count = 0;

for i= 1 : 10000

if (population >=30) && (population<=48)

count = count+1;

end

end

now u have total number of sample between 30 and 48..divide them by 10000 to get required probability , as it follow from relative frequency of occurence.

b. to find arithmtc mean instead of using pdf/cdf : do this ;

mean = sum(population)/10000;

good luck!

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