Lecture 8 - Slide 51, 58

[Fan]

1. On slide 51, the term 'uniqueness' refers to?

2. On Slide 58 of lecture 8, it says 

"If we know that the click probability is < 0.15, then we can bound sigma 2 at 0.15 * 0.85 = 0.1275"

Where does the 0.85 come from, and why do we calculate the bound in this way?

[Barnabas Poczos]

1,
The characteristic function is unique. So if you know that the
characteristic function of a distribution is exp(-x^2/2), then this
implies that the distribution is the normal distribution.

2., 0.85 is the probability of 'no click': 0.85+0.15 =1. We want to
find an upper bound on the variance of Bernoulli(p) when you know that
p<0.15. The variance of Bernoulli(p) is p(1-p). The
variance of Bernoulli(0.15) is 0.15*0.85. Using this,
you can prove that Var(Bernoulli(p))<0.15*0.85 if p<0.15.

Let me know if you have more questions.

Barnabas

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