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Homework A
• Suppose we have an unfair coin and wish to estimate the outcome (head or
tail) from observing a series of coin tosses.
• q = probability of tossing a head.
• After observing n coin tosses, we note that:

D  x (1) ,
, x(n)

where x(i) is 0 or 1, indicating head (0) or tail (1). We also note that in
our data set, h trials are head.
• Show that: q ML 
h
n
Homework B
• For a random variable x that was described by an exponential distribution
we have:
1
 1

p x(i ) a  exp   x(i ) 
a0
a
 a



1 n (i )
aML 
x
n i 1

• Show that this estimator is unbiased. Hint: You need to show that the
expected value of the random variable under this distribution is the ML
estimate.