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2d
revised How do I calculate probability of drawing cards in a certain order?
added 314 characters in body
2d
revised Solutions to a quadratic diophantine modular equation
added 3 characters in body
2d
answered How do I calculate probability of drawing cards in a certain order?
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comment 95% Confidence Interval Problem for a random sample
Unsatisfactory answer, because the distribution of the statistic you used is $t$ with $n-1$ degrees of freedom, where $n$ is the sample size. And make sure to use the two-tailed test, $0.025$ in each tail.
2d
comment 95% Confidence Interval Problem for a random sample
I looked, you used $t$ table, $25$ degrees of freedom. It should be $24$.
2d
comment Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
Not quite. though a small twist on that solution will do it.
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comment Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
No, I find searching MSE too difficult.
2d
comment Each number in a subset $S\subseteq \{1,\ldots,2n\}$ does not divide another one. Then $\max |S|$?
With $100$ instead of $1000$, a golden oldie that has appeared more than once on MSE.
2d
answered Solutions to a quadratic diophantine modular equation
2d
comment For a natural number b, N(b)= number of natural numbers a such that the equation x2+ax+b=0 has integral roots.
Well written up. congratulations.
2d
comment For a natural number b, N(b)= number of natural numbers a such that the equation x2+ax+b=0 has integral roots.
Hint: Think about the product of the roots.
2d
comment probability that 5 square lie along a diagonal line - doubt
One would first need a precise statement of the problem, and in particular what choices are allowed. For the same bunch of $5$, can one use different sizes? For single chess-type squares, and $n$ by $n$, the strategy used by Brian Scott works smoothly.
2d
awarded  Necromancer
2d
comment probability that 5 square lie along a diagonal line - doubt
Sure, if they overlap. But I think the default interpretation of "square" in that problem is one of the $64$ chessboard squares.
Aug
25
awarded  Nice Answer
Aug
25
comment Do the bounds change when multiplying a probability distribution by a constant?
The question is quite unclear. What does it mean to multiply a probability distribution by a constant?
Aug
25
comment Where did I go wrong in my evaluation of the integral of cosine squared?
You are welcome. I made another integration by parts suggestion in a comment above.
Aug
25
comment Where did I go wrong in my evaluation of the integral of cosine squared?
If you want to use integration by parts, it is easier to let $u=\cos x$, $dv=\cos x\,dx$. Then you get $I=\sin x\cos x+\int\sin^2 x\,dx$. Replace $\sin^2 x$ by $1-\cos^2 x$.
Aug
25
answered Where did I go wrong in my evaluation of the integral of cosine squared?
Aug
25
comment Definition of triangle
Some people call it a degenerate triangle. I hope its feelings are not hurt.