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What will happen when one toss a coin many times?

Probability is a good way of talking about information.

There’re many ways of talking about information, but basically it’s more about new things that cannot be predicted. i.e. What I don’t know about the world?

It talks about statistic property & probability.

A biased coin: a. pictures of a dark room (b/w), more 1s than 0s.

b. noise, more 0s than 1s

Data compression:

n lossless source coding

n rate-distortion theory. i.e. images(within some error, compress as much as one can)

Problem Set 1

Independence c.d.f. cumulative distribution function of x.

Pr(x <= x) = f(x)

Two random variables X and Y are independent if and only if

P(X <= x, Y <= y) = P(X <= x)P(Y <= y)

When there’re 3 variables. Each two of them can be independent with each other but the three of them are dependent.

i.i.d. identical & independently distributed.

How many different sequences there are for tossing a coin ten times? 2^10

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