# Tag Info

Accepted

• 4,244
Accepted

### Strong invariance principles

The sequence $\{S_n\}$ has the same almost sure properties as the sequence $\{S_n'\}$ and more generally for any measurable set $A$ in sequence space the chance that $\{S_n\}$ is in $A$ equals the ...
• 13.7k
1 vote

### Hypothesis test, finding p-value

$H_{0}: X \sim \mathcal{N}( 0,5;\ \ 5\cdot 0,5 \cdot (1-0,5))= \mathcal{N}(0,5;\ \ 1,25).$ $p-value = P(\{X >0,8\}) = 1 - P(\{Z\leq \frac{0,8-0,5}{\sqrt{1,25}}\}) = 1 -\phi(0,2683)= 0,3942.$
• 19
1 vote
Accepted

### Confused on approximation of Binomial using Normal distribution

Here I have plotted the PMF of the binomial distribution with parameters $n = 100$, $p = 0.12$, which is represented as the blue shaded region, and the normal approximation with mean $\mu = np = 12$ ...
• 113k

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