How to calculate success probability p(This can and should be solved without using results about summing geometric series. Use the distribution function F.) Y is a geometric random variable with P ( Y ≥ 11 ) = 0.1, determine the following.a) The value of the Success probability pb) P ( 5 &lt; Y &lt; 15 )

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How to calculate success probability p(This can and should be solved without using results about summing geometric series. Use the distribution function F.) Y is a geometric random variable with   P  (  Y  ≥  11  )  =  0.1, determine the following.a) The value of the Success probability pb)   P  (  5  &amp;lt;  Y  &amp;lt;  15  )

Mekhi Parker · Accepted Answer

Step 1At a) we have to assume that   P  (  Y  =  0  )  &amp;gt;  0. So the pdf is   P  (  Y  =  k  )  =  (  1  −  p      )    k    ⋅  pThis is the second version of the geometric distribution. k is the number of failures until the first success. The cdf is  P  (  Y  ≤  n  )  =      ∑          k      =      0        n    (  1  −  p      )    k    ⋅  pNow it seems that you have to calculate   P  (  Y  ≥  1  ), not 11 (typo I think). Here you can use the converse probability.  P  (  Y  ≥  1  )  =  1  −  P  (  X  =  0  )  =  1  −  (  1  −  p      )    0    ⋅  p  =  0.1Now it is easy to see what p is.Step 2At b) you have to sum up all the required probabilities  P  (  5  &amp;lt;  Y  &amp;lt;  15  )  =  P  (  6  ≤  Y  ≤  14  )  =      ∑          k      =      6              14        (  1  −  p      )    k    ⋅  p

This can and should be solved without using results about summing geometric series. Use the distribution function F.) Y is a geometric random variable with P(Y >=11)=0.1, determine the following. a) The value of the Success probability p. b) P(5<Y<15)

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