Question

What is Converjence in probability???​

Answer 1

Explanation:

• The concept of convergence in probability is based on the following intuition: two random variables are "close to each other" if there is a high probability that their difference is very small. Let be a sequence of random variables defined on a sample space. Let be a random variable and a strictly positive number

Answer 2

Topic :- convergence in probability

Information :-

Convergence in probability is stronger than convergence in distribution. In particular, for a sequence X1X1, X2X2, X3X3, ⋯⋯ to converge to a random variable XX, we must have that P(|Xn−X|≥ϵ)P(|Xn−X|≥ϵ) goes to 00 as n→∞n→∞, for any ϵ>0ϵ>0. To say that XnXn converges in probability to XX, we write

Formual :-

Xn →p X.

Xn →p X.

Here is the formal definition of convergence in probability:

Convergence in Probability

More to know :-

A sequence of random variables X1X1, X2X2, X3X3, ⋯⋯ converges in probability to a random variable XX, shown by Xn →p XXn →p X, if

limn→∞P(|Xn−X|≥ϵ)=0, for all ϵ>0.

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