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Sep
29
answered $\int_0^\infty x \, \lambda e^{-\lambda x} \, dx$
Sep
29
revised How to solve an equations?
added 13 characters in body
Sep
29
comment How to solve an equations?
$$- \frac{-1}{ x+a_{{0}}}+ \frac{-1}{x+a_{1}}+{ \frac {b_{{0}}}{ \left( x+a_{{0}} \right) ^{2}}}+{\frac {b_{{1}}}{ \left( x+a_{{1}} \right) ^{2}}}={\frac {-2\,{x}^{3}+ \left( -3\,a_{{0 }}-3\,a_{{1}}+b_{{0}}+b_{{1}} \right) {x}^{2}+ \left( -{a_{{0}}}^{2}-4 \,a_{{0}}a_{{1}}+2\,a_{{0}}b_{{1}}-{a_{{1}}}^{2}+2\,a_{{1}}b_{{0}} \right) x-{a_{{0}}}^{2}a_{{1}}+{a_{{0}}}^{2}b_{{1}}-a_{{0}}{a_{{1}}}^ {2}+{a_{{1}}}^{2}b_{{0}}}{ \left( x+a_{{1}} \right) ^{2} \left( x+a_{{0 }} \right) ^{2}}} $$
Sep
29
comment How to solve an equations?
Even $N=1$ gives you a cubic.
Sep
29
comment How to solve an equations?
What makes you think it will be quadratic?
Sep
29
answered How to solve an equations?
Sep
29
answered Second-order Non-linear ODE IVP
Sep
29
comment Second-order Non-linear ODE IVP
Since this is a second-order DE, you have one too many initial conditions.
Sep
29
answered Is it possible for $b[x;r) = b[y;s)$ when $x \neq y$ and $r \neq s$?
Sep
27
awarded  Enlightened
Sep
27
awarded  Nice Answer
Sep
27
awarded  convergence
Sep
26
comment What is an intuitive definition of the zero vector?
If a nonempty subset is closed under scalar multiplication, it necessarily contains the zero vector ($0 {\bf x} = \bf 0$)
Sep
25
answered How to integrate a function that has no exact integration and cannot be expanded by a Taylor series
Sep
25
answered What are the correct interpretations for these basic probability questions?
Sep
25
comment I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?
If each of the approximately $7$ billion people on earth generated an independent normally distributed random variable once a second (and the population stayed constant), the expected time until one of those random variables was more than $10$ standard deviations from the mean would be about $300,000$ years.
Sep
25
comment I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?
so it's outside that range about $15$ times in every septillion.
Sep
25
comment I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?
... and it is between $\mu - 10 \sigma$ and $\mu + 10 \sigma$ with probability about $1 - 1.52 \times 10^{-23}$.
Sep
25
answered Finding variance .
Sep
25
comment Finding variance .
...and that's exactly $\int_0^1 f(x)\; dx - \left(\int_0^1 f(x)\; dx\right)^2 = I - I^2$.