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Expected value with condition

  1. May 26, 2013 #1
    the random value X takes values 1,2,3.... and has the X has geometric distribution with p=0.20 (This means that X can be interpreted as the time the first crown to repeated throws a coin coin lands heads with probability p.) what is the expected value E(X/X>=6)=?

    i use this type : E(X/X>=6)=sum(k*P(X=k/X>=6))
    but how i can estimate this> how i will find P(X=k and X>=6)=? and P(X>=6)=? where k=1,2,3...
  2. jcsd
  3. May 26, 2013 #2


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    P(X = k) = (1-p)^{k-1}p

    You can easily find the value of [itex]P(X \ge 6)[/itex] by realising that [itex]P(X \ge 6)=1-P(X<6)[/itex], which is computationally simple to evaluate (or use the equation for the cumulative distribution function, which you can find with a quick Google search).

    [itex]P(X=k \cap X \ge 6)[/itex] is quite simple if you consider particular values of k. What is its value if [itex]k<6[/itex]? What about when [itex]k \ge 6[/itex]?
  4. May 26, 2013 #3

    I like Serena

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    What does the condition X>=6 mean in words?
    What can you say about expectation of the number of additional throws required?

    If you understand it, you can see the answer immediately.
  5. May 26, 2013 #4
    i found the P(X>=6) but i cant find the P(X=k AND x>=6) i sum all them :sum from k=6 to inf of p*(1-p)^(k-1) bt its not correct...
  6. May 26, 2013 #5

    Ray Vickson

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    For k < 6, what is the event {X = k and X >= 6}? (Never mind about probabilities for now; just answer my question about the event. For k = 6, what is the event {X = k and X >= 6}? For k > 6, what is the event {X = k and X >= 6}?

    As I said, answer these questions first, then worry afterwards about probabilities.
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