**Mumbai University > Electronics and Telecommunication Engineering > Sem 5 > Random Signal Analysis

Marks: 10M

Year: May 2016

Weak Law of Large numbers:

Let $X_1$,$X_2$,$X_3$…..$X_n$ be a sequence of independent identically distributed RVs each with finite mean E($X_i$ )=μ

Let ${X_n }^{ ̅ }$=1($X_1$+$X_2$+⋯.$X_n$)/n

then for any ∈>0P $lim_{n→∞}$ P(|${X_n }^ ̅ $-μ|>∈)=0 ..................... (1)

This is known as weak law of large numbers and $(X_n )^ ̅ …