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Math Help - Toss a fair coin until you get a head, or five consecutive tails, whichever comes...

  1. #1
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    Toss a fair coin until you get a head, or five consecutive tails, whichever comes...

    Toss a fair coin until you get a head, or five consecutive tails, whichever comes first. Define the random variable X= # of tosses.

    A.) Determine the pmf for this random variable & variety that it satisfies the two conditions for a pmf.

    B.) Find E(X)

    C.) Find Var(x) and the Standard deviation.

    A.) I have included a picture showing my work.

    for B. I found the expectation of X to be equal to 62, work shown in photo.

    C. I attempted this part but I'm unsure if it is correct
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  2. #2
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Toss a fair coin until you get a head, or five consecutive tails, whichever comes...-image.jpg
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  3. #3
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Quote Originally Posted by grandmarquis84 View Post
    Toss a fair coin until you get a head, or five consecutive tails, whichever comes first. Define the random variable X= # of tosses.

    A.) Determine the pmf for this random variable & variety that it satisfies the two conditions for a pmf.

    B.) Find E(X)

    C.) Find Var(x) and the Standard deviation.

    A.) I have included a picture showing my work.

    for B. I found the expectation of X to be equal to 62, work shown in photo.

    C. I attempted this part but I'm unsure if it is correct
    looks like you worked the problem with heads and tails reversed.

    I don't see the distribution listed clearly anywhere. You don't show the sum of the distribution values equals 1.

    I have no idea what those e's are. Your expected value is incorrect.

    I don't see any work for part c.
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  4. #4
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Sorry, my picture for part c. Didn't seem to upload. Although now knowing b.) is in correct it seems to be pointless to post it since I can't figure it out without properly computing the expectation
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  5. #5
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Hmm I think I accidentally calculated the expectation for getting 5 consecutive tails in a row and accidentally ignored the head portion. I think the expectation is approx 1.93 heads or 2 heads wen rounded
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Quote Originally Posted by grandmarquis84 View Post
    Hmm I think I accidentally calculated the expectation for getting 5 consecutive tails in a row and accidentally ignored the head portion. I think the expectation is approx 1.93 heads or 2 heads wen rounded
    the possible #of tosses is 1-5. Show the probability of each of these.
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  7. #7
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    I think I worked out the problem. Any confirmation, or help if I made a mistake is appreciatedToss a fair coin until you get a head, or five consecutive tails, whichever comes...-image.jpg
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  8. #8
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Quote Originally Posted by grandmarquis84 View Post
    I think I worked out the problem. Any confirmation, or help if I made a mistake is appreciatedClick image for larger version. 

Name:	image.jpg 
Views:	3 
Size:	1.05 MB 
ID:	30724
    much better.

    Everything looks correct but I get a slightly different answer for the variance. I get 1.43 rather than 1.36. You might check your figures.
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  9. #9
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    It is correct, but I don't see part (A). While I can figure out implicitly what you are using for your pmf, you should explicitly write it out.
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  10. #10
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Toss a fair coin until you get a head, or five consecutive tails, whichever comes...-image.jpg thank you, sorry I didn't realize part a didn't post
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  11. #11
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    picky I know but show they sum to 1
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  12. #12
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    Re: Toss a fair coin until you get a head, or five consecutive tails, whichever comes

    Sounds good thank you, better to have 100% rather than run the risk of not showing enough work after all
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