A weather forecaster predicts that the may rainfall in a local area will be between three and six inches but has no ides where within the interval the amount will be. Let x be the amount of M ay rainfall in the local area, and assume that x is uniformly distributed over the interval three to six inches. What is the probability that May rainfall will be at least four inches? At least five inches?

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A weather forecaster predicts that the may rainfall in a local area will be between three and six inches but has no ides where within the interval the amount will be. Let x be the amount of M ay rainfall in the local area, and assume that x is uniformly distributed over the interval three to six inches. What is the probability that May rainfall will be at least four inches? At least five inches?

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Answer:- Let x be the amount of May rainfall in the local area, and assume that x is uniformly distributed over the interval 3 to 6 inches. 

That is, X~ U( 3, 6) 

So, pdf of X is 

f(x) = 1/(b-a) = 1/(6-3) = 1/3 

And The cdf of X is , 

P( X ≤ x) = (x-a)/(b-a) = (x-3)/3

 

 

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