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Dec
15
comment Series and Sequences Train Question
The use of the word ratio is very peculiar in this context. It should be constant acceleration (or deceleration),
Dec
15
comment Approximate using the central limit theorem
Sure, lots of standard deviation units away. Can't happen.
Dec
15
comment Approximate using the central limit theorem
You have some wrong numbers, for example the mean is $60$. Also, I would calculate $\Pr(W\le 101)-\Pr(W\le 98)$ where $W$ is the approximating normal (well, I am lying, I would use the continuity correction, but we have been told not to).
Dec
14
comment Find expectation and variance
(i) Always, $E(X+Y)=E(X)+E(Y)$; (ii) If $X$ and $Y$ are independent, $E(XY)=E(X)E(Y)$; (iii) If $X$ and $Y$ are independent then $\text{Var}(X+Y)=\text{Var}(X)+\text{Var}(Y)$.
Dec
14
comment Find the probability density function of $Y = 4X_1 – X_2$
There is a full answer now posted, so it is unnecessary.
Dec
14
comment Find the probability density function of $Y = 4X_1 – X_2$
A linear combination of independent normals is normal. Now all you need to do is compute the mean and variance,
Dec
14
comment Is Infinity the limit?
How can one expect to prove a meaningless assertion?
Dec
14
comment derivatives $\frac{dy}{dx}$
Let $V=V(t)$ be the volume of sand in the box at time $t$, and let $z=z(t)$ be the height of the sand in the box at time $t$. We know $\frac{dV}{dt}$ and want $\frac{dz}{dt}$. Find a relationship between $V$ and $z$, and differentiate.
Dec
14
comment How many finite sequnces $x_1,x_2,x_3,\ldots,x_m$ are there such that $x_i =1$ or $2$ and $\sum_{i=1}^{m}x_i=10$
Depends on how one indexes. But under the more common indexing, yes.
Dec
14
comment How many finite sequnces $x_1,x_2,x_3,\ldots,x_m$ are there such that $x_i =1$ or $2$ and $\sum_{i=1}^{m}x_i=10$
@user103828: Yes, it is the Fibonacci number $F_k$, for which you can give a closed form (Binet Formula).
Dec
14
revised How many finite sequnces $x_1,x_2,x_3,\ldots,x_m$ are there such that $x_i =1$ or $2$ and $\sum_{i=1}^{m}x_i=10$
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Dec
14
answered How many finite sequnces $x_1,x_2,x_3,\ldots,x_m$ are there such that $x_i =1$ or $2$ and $\sum_{i=1}^{m}x_i=10$
Dec
14
comment Trig sub and Integration of Squareroot divided by polynomial squared
Early on, slip, you should end up with $\int \frac{\cos^2\theta}{\sin^2\theta}\,d\theta$, you have twice that. So you are integrating $\cot^2\theta$, that is, $\text{cosec}^2\theta-1$.
Dec
14
answered How to prove a right angle if i have two tangents?
Dec
14
comment Question about proving $\displaystyle\lim_{n\to\infty} n=\infty$ using the limit definition for a converging sequence
Git Gud is absolutely right, proving the result is easy, but certainly not acieved by showing there is no finite limit.
Dec
14
comment Word problem related to normal distribution
No trick. As to without tables or software, some people might expect their students to remember certain key entries of the table.
Dec
14
revised How can I prove the last digit of $(2^{121985292}-1)$ is $5$
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Dec
14
revised There are 10 stations on a circular path
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Dec
14
answered There are 10 stations on a circular path
Dec
14
comment Summing of factorials to produce perfect cubes
@WillJagy: Apologies about the very minor edit. The reason for it is that I had inadvertently downvoted instead of upvoting. Touchscreen, it has happened more than once. By the time I noticed, it could not be reversed unless the thing was edited.