A distribution with unknown mean μ has variance equal to 1.5. Use central theorem to find how large a sample should be taken from the distribution in order that the probability will be at least 0.9 that the sample mean will be within 0.5 of the population mean.

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

Marks: 10M

Year: May 2016

If $X_1$,$X_2$,$X_3$…..$X_n$ be a sequence of independent identically distributed RVs with E($X_i$ )=μ and Var ($X_i$) =$σ^2$, i=1,2…. and if $S_n$=$X_1$+$X_2$+⋯.$X_n$, then under certain general conditions, $S_n$ follows a normal distribution with mean nμ and variance $nσ^2$ as n tends to infinity.

Corollary:

If X ̅ =1($X_1$+$X_2$+⋯.$X_n$)/n, then E(X ̅ …