Statinference
Probability
 Population quantity summarizing the randomness of a random experiment
 Inherently when we are talking about probability we are talking about population
 Data in hand is just an aid to model this probability
 $\alpha$ quantile: $F(x_\alpha)=\alpha$ About%100(1\alpha)$ of the observations lie above this point
Baye’s Rule

$P(B A)=\frac{P(A B)P(B)}{P(A B)P(B)+P(A B^c)P(B^c)}$  Let

 = Test results positive

 = Test results positive
 D = Person has disease in reality
 D^c = Person does not have disease


Sensitivity = $P(+ D)$ 
Specificity = $P( D^c)$ 
Positive Predictive Value(PPV) = $P(D +)$ 
Negative Predictive value = $P(D^c )$  Prevalence of Diseae = $P(D)$

Likelihood ratio: $\frac{P(D +)}{P(D^c +)}= \frac{P(+ D)P(D)}{P(+ D^c)P(D^c)}$  Post test odds of D = $DLR_+$ x Pre test odds
Estimation
 Sample mean is itself a random variable and will have it;s own distribution, expected value
 The center of this distribution of the sample mean is same as that of observation making the sample mean an ‘unbiased’ estimator of population mean
 Expected values are properties of distribution
 Sample mean is an estimate of pipulation mean.
 Center of mass of population = population mean
 Center of mass of observations  Sample mean