2.1 ( ) www Verify that the Bernoulli distribution (2.2) satisfies the following properties 1 x=0 p(x|) = 1 (2.257) E[x] = (2.258) var[x]

2.1 () www Verify that the Bernoulli distribution (2.2) satisfies the following properties

1 x=0 p(x|μ) = 1 (2.257)

E[x] = μ (2.258)

var[x] = μ(1 − μ). (2.259)

Show that the entropy H[x] of a Bernoulli distributed random binary variable x is given by H[x] = −μ ln μ − (1 − μ) ln(1 − μ). (2.260)