Henry
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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