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6h
comment Number of chords of a circle having natural length
@HamidRezaEbrahimi: The length of the chord is a continuous function of the angle of the chord, so it achieves all intermediate values at some angle. See en.wikipedia.org/wiki/Intermediate_value_theorem
6h
comment Number of chords of a circle having natural length
One for $34$, one for $16$ and two for every integer between them
6h
comment Probabilities playing bridge
Since your answers are all multiples of $\frac{1}{160}$, there might be a way which avoids such a big multiplication
6h
comment Number of chords of a circle having natural length
@almagest: I would guess "natural length" means a natural number, i.e. an integer
6h
answered Number of chords of a circle having natural length
14h
answered Find center of circle with 2 internally touching circles
15h
comment why mixed normal distribution has heavier tail than normal distribution?
What makes you think it is true?
22h
comment Estimating distribution from two distributions
You can find the mean of the $Y_i$
23h
comment How to determine parameters of a normal distribution from a limited range of points?
How do you know your data is normally distributed if you can only observe the right tail?
1d
revised Optimal bet according to the probability of win
direction
1d
comment How to prove convergence? $Y_n= X_{n+1}-X_n$
Difficult to prove "only if"
1d
comment Questions on probability law
I find many of your arguments unconvincing, especially (3) and (6), while for (2) I think need the word symmetric
1d
revised Optimal bet according to the probability of win
added 149 characters in body
1d
answered Optimal bet according to the probability of win
1d
answered Triangle with a bisected side and a trisected side
1d
comment Solving for a negative exponent
If you know all the other values, you can find $n$, using logarithms
2d
comment Can distributions scale to any given time scale?
As you say, a warning value of $\frac{5}{60}=0.0833\ldots$ calls per minute does not make much sense: it would give the same alarms as one of $\frac{40}{60}=0.6666\ldots$ calls per minute, and so could produce too many false alarms. What you might want to consider is its reciprocal: might warning after $\frac{60}{5}=12$ minutes without a call produce too many false alarms or too few true alarms? In answer to your title question: it depends, and you have shown a case where using integers leads to the answer no.
2d
comment Use Chebyshev’s inequality to choose $n$ such that $P(\bar{X} > 4) > 0.9$
A one-sided version of Chebyshev’s inequality could give give you a slightly smaller $n$, but assuming $\bar{X_n}$ stands for the sample mean of $n$ i.i.d. random variables, it would still be too high
2d
comment Probability of a number in the real line
You are more likely to have read the picking a number uniformly at random from the interval $[0,1]$ gives you a probability $1$ of picking an irrational number, and a probability $0$ of picking a rational number. Both are dense
Apr
30
comment Shape of distribution between arrivals in a poisson process
@Ian - it depends on whether $T_2$ is the arrival time of the second event, or the interarrival time between the first and second events