Question: The memoryless property. Suppose F has geometric distribution on {0, 1, 2, .. }.
a) Show that for every k > 0, P(F-k = m | F > k) = (F = m), m = 0, 1, . .
b) Show the geometric distribution is the only discrete distribution on {0, 1, 2, . .} with this property.
c) What is the corresponding characterization of the geometric (p) distribution on {1, 2, . .)?