Suppose a researcher is studying the number of sexual acts with an infected person
until an uninfected person contracts an sexually transmitted disease. She assumes
that each encounter is an independent Bernoulli trial with probability p that
the subject becomes infected. This leads to the so-called geometric distribution
P(Person is infected on contact x) = p(1 − p)
x−1
for x = 1, . . ..
1
a. Suppose that one subject’s number of encounters until infection is recorded, say
x. Symbolically derive the ML estimate of p.
b. Suppose that the subjects value was 2.

Question

Suppose a researcher is studying the number of sexual acts with an infected person
until an uninfected person contracts an sexually transmitted disease. She assumes
that each encounter is an independent Bernoulli trial with probability p that
the subject becomes infected. This leads to the so-called geometric distribution
P(Person is infected on contact x) = p(1 − p)
x−1
for x = 1, . . ..
1
a. Suppose that one subject’s number of encounters until infection is recorded, say
x. Symbolically derive the ML estimate of p.
b. Suppose that the subjects value was 2.