Suppose that lions have a geometric offspring distribution. p k = ( 1 − θ ) θ k , k ≥ 0 with mean 1.5. If the current world population of lions is 10, what is the probability they will go extinct in 1 generation? What is the probability they will go extinct eventually?Same two questions whose offspring distribution is Poisson with mean 0.8, and current population is 5000.

Question

Suppose that lions have a geometric offspring distribution.       p          k        =  (  1  −  θ  )      θ          k      ,   k  ≥  0 with mean 1.5. If the current world population of lions is 10, what is the probability they will go extinct in 1 generation? What is the probability they will go extinct eventually?Same two questions whose offspring distribution is Poisson with mean 0.8, and current population is 5000.

Caiden Brewer · Accepted Answer

Step 1Suppose every member gives birth independently to an identically distributed number of &quot;children&quot;, X is the number of offspring. If   P  (  X  =  0  )  &amp;gt;  0  P  (  t  h  e     p  r  o  c  e  s  s     w  i  l  l     g  o     e  x  t  i  n  c  t  )  =  1    ⟺           E    X  ≤  1Step 2When       E    X  &amp;gt;  1, and you want to compute P(the process will go extinct), then you need to use the generating function for X.

Suppose that lions have a geometric offspring distribution. p_k=(1-theta) theta^k, k ge 0 with mean 1.5. If the current world population of lions is 10, what is the probability they will go extinct in 1 generation? What is the probability they will go extinct eventually?

Answered question

Answer & Explanation

New Questions in High school geometry