Question

the integers from 1 to n are assigned probabilities proportional to their sizes. find the conditional probability of 1 given that 1 to n occurs​

Answer 1

Answer:

The formula for conditional probability is derived from the probability multiplication rule, P(A and B) = P(A)*P(B|A). You may also see this rule as P(A∪B). The Union symbol (∪) means “and”, as in event A happening and event B happening.

Step-by-step explanation:

Let P be a finite population with N≥1 elements; for each e∈P, let Xe and Ye be independent, positive random variables with unknown distribution functions F and G; and suppose that the pairs (Xe,Ye) are i.i.d. We consider the problem of estimating F,G, and N when the data consist of those pairs (Xe,Ye) for which e∈P and Ye≤Xe. The nonparametric maximum likelihood estimators (MLEs) of F and G are described; and their asymptotic properties as N→∞ are derived. It is shown that the MLEs are consistent against pairs (F,G) for which F and G are continuous, G−1(0)≤F−1(0), and G−1(1)≤F−1(1).

√

N

× estimation error for F converges in distribution to a Gaussian process if ∫

∞

0

(1/G)dF<∞, but may fail to converge if this integral is infinite.