Martingales and Financial Mathematics in Discrete Time. Benoîte de Saporta

is 6. Determine the distribution of X6 and then calculate [X6].

      EXERCISE 1.8.– Let p ∈]0, 1[. We have one coin that leads to tails with the probability p. We toss this coin until we obtain tails for the second time. Let X be the number of heads obtained during this experiment.

      1 1) Determine the distribution of X.

      2 2) Justify the existence of the expectation of X.

      3 3) Calculate [X].