Intereting Posts

Mere coincidence? (prime factors)
Prove there is no element of order 6 in a simple group of order 168
Which meromorphic functions are logarithmic derivatives of other meromorphic functions?
Trigonometric/polynomial equations and the algebraic nature of trig functions
Alternative proof that Harmonic sum is not an integer
does this Newton-like iterative root finding method based on the hyperbolic tangent function have a name?
Proving two lines trisects a line
Cancellation of Direct Products
Why isn't an injection defined with an iff?
Rate of convergence of series of squared prime reciprocals
How to prove $\cos ^6x+3\cos ^2x\space \sin ^2x+\sin ^6x=1$
Can someone explain Gödel's incompleteness theorems in layman terms?
Why $\sum_{k=1}^{\infty} \frac{k}{2^k} = 2$?
Methods to evaluate $ \int _{a }^{b }\!{\frac {\ln \left( tx + u \right) }{m{x}^{2}+nx +p}}{dx} $
Exact probability of random graph being connected

Can someone please give me a reference to an (simple, realworld, i.e. not constructed) example of a discrete probability space such that there are three events in it that are pairwise independent but all three together are not independent (although I wouldn’t mind, if someone would give me the example as an answer).

- Probability question with interarrival times
- Summing over conditional probabilities
- Distribution of the lifetime of a system consisting of two exponentially distributed components, one being backup
- Broken stick probability problem
- How do I teach university level mathematics to myself?
- What's the probability that we don't have $3$ consecutive heads in $n$ tosses?
- Cauchy Schwarz inequality for random vectors
- Frequency distribution for N balls in m urns (distributed equiprobably)
- Probability of being able to make a given number with two out of xd6
- Conditional probabilties in the OR-gate $T=A\cdot B$ with zero-probabilities in $A$ and $B$?

The standard example involves tossing $2$ fair coins. For a more symmetrical example, toss $3$ fair coins. Let $A$ be the event Toss $1$ and Toss $2$ give the same result, $B$ be the event Toss $2$ and Toss $3$ give the same result, and $C$ the event Toss $3$ and Toss $1$ give the same result.

We have $\Pr(A)=\Pr(B)=\Pr(C)=\frac{1}{2}$ and $\Pr(A\cap B)=\Pr(B\cap C)=\Pr(C\cap A)=\frac{1}{4}$.

However, it is clear that $A$, $B$, and $C$ are not mutually independent.

http://en.wikipedia.org/wiki/Independence_%28probability%29#Pairwise_and_mutual_independence ${}{}{}{}{}{}{}{}{}{}{}{}{}{}{}$

- Are these exactly the abelian groups?
- Problem with definition of limit (why not big delta?)
- Kolmogorov's sufficient and necessary condition for SLLN – What about pairwise uncorrelated RV?
- The Intersection of Ordered Pairs
- Boundedness of functions in $W_0^{1,p}(\Omega)$
- How to prove the Fibonacci sum $\sum \limits_{n=0}^{\infty}\frac{F_n}{p^n} = \frac{p}{p^2-p-1}$
- Total ordering on complex numbers
- Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.
- Difficult infinite integral involving a Gaussian, Bessel function and complex singularities
- Does the graph of a measurable function always have zero measure?
- Show that there is a step function $g$ over $$
- $(\Bbb Z\oplus \Bbb Z) \not\cong \Bbb Z\oplus \Bbb Z\,$?
- Degree of splitting field divides n!
- Does May's version of groupoid Seifert-van Kampen need path connectivity as a hypothesis?
- Help understanding Algebraic Geometry