Drought length is referred to as the number of consecutive time intervals in which the water supply remains below a critical value. Consider the drought length as a random variable, denoted as Y, which is assumed to have a geometric distribution with p=0.409

heelallev5 2022-08-13 Answered
Geometric or Poisson
Drought length is referred to as the number of consecutive time intervals in which the water supply remains below a critical value. Consider the drought length as a random variable, denoted as Y, which is assumed to have a geometric distribution with p = 0.409
1. What is the probability that a drought lasts exactly 3 intervals? (0.0844)
2. What is the probability that a drought lasts at most 3 intervals? (0.878)
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Answers (1)

Gauge Howard
Answered 2022-08-14 Author has 19 answers
Step 1
The geometric distribution is defined as
P ( Y = k ) = p ( 1 p ) k 1 , k 1
Equivalently: P ( Y > k ) = ( 1 p ) k
Step 2
The first question just asks P ( Y = 3 ), and the second question asks P ( Y 3 ), which we can write 1 P ( Y > 3 )
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