Question

NEED HELP FOR EXAM
Give the probability distribution for the indicated random variable.
A fair coin is tossed three times, and we count the number of "runs" that occur. A "run" is defined as a sequence of one or more of the same letter (e.g., HTH is 3 runs, TTH is 2 runs, and TTT is 1 run).

Answer 1

Underlying distribution is binomial p=1/2, q=1/2.

However, runs require three in a row, so p = (1/2)^3 and q=1-p,
Further, HHH or TTT counts, so must double p to p=(1/2)^2

Answer 2

so i have a table like this

Answer 3

how do you find whats missing?

Answer 4

@douglaswinslowcooper