Assume you have a biased coin with P(T) = 0.4 and P(H) = 0.6. Toss the coin 10 times and toss again whenever a heads is showed. Tosses are independent, and count the cases when there are two consecutive heads.

What is the pmf, expected value, variance, and the support of X, where X is the counted number of double heads?

pur-new-sol