DerivedDistro

Derived Distribution

Compose one or more simple random variables to get more complicated r.v. (This is how we go from simple model to complicated model) ($f(X)$)

Discrete

case

Obvious formula

$$
P_Y(y) = P(Y=y) = \sum_{\text{all x if g(x)=y}} P_X(x)
$$

$$
P_Y(4) = P_X(5)+P_X(4) = 0.4 + 0.3 = 0.7
$$

Linear Example

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Independent

Independence

If event A really happens, it does not change the probability of B( P(B) == P(B|A) ), we say A doesn’t carry any useful information about B, A and B are independent

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