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

1. ## 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

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

Originally Posted by grandmarquis84
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.

4. ## 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

5. ## 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

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

Originally Posted by grandmarquis84
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.

7. ## 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 appreciated

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

Originally Posted by grandmarquis84
I think I worked out the problem. Any confirmation, or help if I made a mistake is appreciated
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.

9. ## 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.

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

thank you, sorry I didn't realize part a didn't post

11. ## 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

12. ## 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