Geometric or PoissonDrought 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 = 0.4091. 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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Geometric or PoissonDrought 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  =  0.4091. 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)

Gauge Howard · Accepted Answer

Step 1The geometric distribution is defined as  P  (  Y  =  k  )  =  p  (  1  −  p      )          k      −      1        ,    k  ≥  1Equivalently:   P  (  Y  &amp;gt;  k  )  =  (  1  −  p      )    k  Step 2The first question just asks   P  (  Y  =  3  ), and the second question asks   P  (  Y  ≤  3  ), which we can write   1  −  P  (  Y  &amp;gt;  3  )

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

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