5
votes
Accepted
Hypothesis test, finding p-value
I think the Central Limit Theorem is a poor approximation here for 5 samples. The exact probability is $P(T \ge t) = P(5T \ge 4) = P(5T = 5) + P(5T = 4) = \frac{1}{2^5} (\binom{5}{0} + \binom{5}{1}) = ...
- 81.8k
2
votes
Accepted
2500 people have a car insurance there are 1500 women and 1000 men. Estimate probability that in the next year there will be at least 25 car accidents
There are versions of CLT that does not require identically distributed random variables. See, e.g, wikipedia and http://personal.psu.edu/drh20/asymp/fall2002/lectures/ln04.pdf.
Let $W_i$, $i = 1,\...
- 4,244
2
votes
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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