Consider the following coin tossing problem. For the first coin toss of each round, the coin lands head with probability . For each toss thereafter, the result matches the outcome of the first toss with probability . Everything resets after the conclusion of each round of coin tosses. For instance, suppose we observed the following results (H heads, T is tails): • Round 1: HHT • Round 2: TTT The probability of observing the sequence of tosses in the first round is $⋅⋅(1−)$ and the probability of observing the sequence of tosses in the second round is $(1−)⋅⋅$. Suppose you have data on rounds of coin tosses with tosses in each round.
Let the number of Tails$=T$ and number of Heads$=H$ The problem asks to write a likelihood function with p,q. for my understanding, the likelihood has two situations: one is $p*q^{H - 1} *(1-q)^{T}$ &the other is $(1-p)*q^{T - 1} *(1-q)^{H}$ but seems is incorrect