Henry
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 9m comment Number of rolls of two fair dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36 @JulietaR: Using Chebyshev's inequality will give a weak approximation as you will be looking to use $\Pr(|X-\mu|\geq k\sigma) \leq \frac{1}{k^2}$ so you want $\frac{1}{k^2} \le 1-0.9$ and $k\sigma = \frac1{36}$ with $\sigma = \sqrt{\frac{5}{36n}}$, leading to $n \ge 1800$, which is much higher than necessary. 21m comment Number of rolls of two fair dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36 @JulietaR: (b) If this is a school exercise then I suspect that the approximation $487$ is the desired answer. All I was doing with the exact answer was demonstrating that this is indeed an approximation, and using a discrete calculation shows counter-intuitively that in a small range using a slightly larger sample size does not always increase the probability of being in the given interval, though the changes are small. 27m comment Number of rolls of two fair dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36 @JulietaR: (a) With a normal distribution, the probability of being above $\Phi^{-1}(0.95)\approx 1.644854$ standard deviations above the mean is $5\%$. Similarly the probability of being below $1.644854$ standard deviations below the mean is $5\%$. So the probability of being within $1.644854$ standard deviations of the mean is $90\%$, and that is how $\Phi^{-1}(0.95)$ is used to find a $90\%$ two-tailed interval. 33m revised Number of rolls of two fair dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36 Invert standard normal 9h comment Distribution and convergence of two random variables 9h answered Number of rolls of two fair dice to be 90% certain that the percentage of times they show the same face is between 5/36 and 7/36 10h revised Prove the following limits without using l'Hospital and Sandwich theorem edited tags 10h comment Probability of 2 cards drawn By symmetry, the probability that the third card drawn is an Ace is equal to the probability that the first card drawn is an Ace. 11h comment Prove that the function is uniformly distributed. $P\left(X^{n}=\frac{k}{n}\right)=\frac1n$ or $P\left(X_{n}=\frac{k}{n}\right)=\frac1n$ ? 11h comment Find the volume of the solid by rotating the region It will be the same as the volume of the solid obtained by rotating the region bounded by the curves $y=x-x^2$ and $y=0$ about the $x$-axis. 11h answered Floor and Ceiling functions 19h comment If $a_n$ is a null sequence, does $\sum^{\infty}_{n=1}a_n$ converge? Your approach is incorrect. If $c_n = a_n-a$ and $d_n=b_n-a$ then you can show $d_n= \frac{1}{n}\sum^{n}_{k=1}c_k$. So you now have $\lim_{n\to\infty}c_n =0$ and you want to show $\lim_{n\to\infty}d_n=0$, which is not the same as showing $\lim_{n\to\infty}\sum^{n}_{k=1}c_k = \lim_{n\to\infty}n d_n =0$. 19h comment coupon collector's problem stirling Do you know the generating function for Stirling numbers of the second kind? I suspect the final result is something like $P(X=m)=S_2^{\,}(m-1,n-1) \dfrac{ n!}{n^m}$ 1d answered Number of Taxicab routes in a triangular city 1d revised Number of Taxicab routes in a triangular city image 1d revised Number of Taxicab routes in a triangular city images 1d comment Gaussian Random Variables Transform into a Rayleigh @A.S. - I might write $\sqrt{\chi_2^2}$ as $\chi_2^{\,}$, the chi distribution with $2$ degrees of freedom 1d comment How do you prove that the quadratic formula workes without doing millions of examples? By completing the square 2d comment Online resources for learning Mathematics That, and the associated mathtutor.ac.uk site, are more pre-undergraduate in UK terms, though still worthwhile 2d answered Covariance formula to find $\sigma(1)$