3.7 Consider N independent binary random variables Y1,...,YN with P(Yi = 1) = i and P(Yi = 0) = 1i . The probability function of

3.7 Consider N independent binary random variables Y1,...,YN with P(Yi = 1) = πi and P(Yi = 0) = 1−πi

.

The probability function of Yi

, the Bernoulli distribution B(π), can be written as

π

yi i

(1−πi)

1−yi

, where yi = 0 or 1.

a. Show that this probability function belongs to the exponential family of distributions.

b. Show that the natural parameter is