What is Converjence in probability?
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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.
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.Convergence in probability -
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Here is the formal definition of convergence in probability: Convergence in Probability. A sequence of random variables X1, X2, X3, ⋯ converges in probability to a random variable X, shown by Xn p→ X, if limn→∞P(|Xn−X|≥ϵ)=0, for all ϵ>0.