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
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.
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
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