If I enter the values ##a_{1}\, = \, 0.7##, ##a_{0}\, = \, 0.4##, ##c_{1}\, = \, 0.9##, ##c_{0}\, = \, 0.5## and ##M\, = \,7## in
$$\int_{0}^{M}\!{y}^{{\frac {c_{0}}{a_{0}}}} \left( M-y \right) ^{{\frac {Mc_{1}}{a_{1}}}}\,{\rm d}y$$
I get ## 17939559.61##. If I enter the same values...
I am looking for a solution of the following integral
$$\int_{-\infty }^{\infty }\!{y}^{k}{{\rm e}^{-{\frac {u_{{0}} \, {{\rm e}^{-y}}}{a_{{0}}}}-{\frac {u_{{1}} \, {{\rm e}^{y}}}{a_{{1}}}}}}\,{\rm d}y$$
with ## 0<a_{0}##, ## 0<a_{1}##, ## 0<c_{0}##, ## 0<c_{1}## and ##k = 1, 2, 3, ..., ##.
How to solve the following integral (in Maple notation):
Int(y**k*exp(-u[0]*exp(-y)/a[0]-u[1]*exp(y)/a[1]),y=-infinity..infinity)
with 0<a[0], 0<u[0], 0<a[1], 0<u[1]?
I have the following integral (in Maple notation):
Int(exp(c[0]*ln(y)/a[0]+c[1]*M*ln(M-y)/a[1]), y = 0 .. M);
with (in Maple notation):
0<a[0], 0<a[1], 0<c[0], 0<c[1], 0<y, y<M, 0<M.
What is the solution of this integral? I suspect that the solution has something to do with a beta distribution.
For a random variable Ti,
SD (Ti) / E (Ti) ≤ 1
with SD (Ti) = (Var (Ti))1/2 and E (Ti) the expectation of Ti and Var (Ti) the variance of Ti. My question now is whether the following property then also applies. For any variable T,
SD (T) / E (T) ≤ 1
where T = T1 + T2 + ... + TN and where...
In a paper published in the JOURNAL OF MATHEMATICAL PSYCHOLOGY 39, 265-274 (1995), formulas are provided on page 272 for the expectation E(Tn) of a random variable T as dependent on n (formulas 28 and 29). Now I would like to know what these formulas look like for the variance i.e. Var(Tn).
Thanks a lot for your clear answer.
I have performed the transformation and I got (in Maple notation):
g (x) = (1/2) * (1 / ((3/2) * Pi)) * (sin ((1/2) * (x- (3/2) * Pi))) ** 2
with support [(3/2) * Pi; (15/2) * Pi)]
but this function coincides completely with the following function:
h (x)...
I have the following probability density function (in Maple notation):
f (x) = (1 / ((3/2) * Pi)) * (sin (x)) ** 2 with support [0; 3 * Pi]
Now I want to transform x so that
0 -> (3/2) * Pi
and
3 * Pi -> (15/2) * Pi
and the new function is still a probability density function.
How should I...
Yes, the nature of the transformation is simply shifting and stretching the interval, but my question was how should you make the transformation for an arbitrary probability density function?
Given the support [a, b] of a probability density function. How can I change the formula for the probability density function with a support [u, v]? Example: Given the beta distribution with support [a=0,b=1]:
$$\frac{x^{p-1} (1-x)^{q-1}}{Beta(p,q)}$$
Then the beta distribution with support...
Sorry, You are right. It should be
$$-a*A/(b/c+1)<0$$
and therefore
$$a*A/(b/c+1)>0$$
and because 0 < a, 0 < b, 0 < c, 0 < A it follows that
$$a*A/(b/c+1)>0$$
is always true.
Am I correct?
@Dale You can distinguish two types of why questions within a science: questions that can or cannot be answered with the current state of affairs and questions that can or cannot be answered by that science in principle. I was talking about why questions of the latter type.
Dale you said:
"In general, science can only answer 'why' questions by appeal to theory, and in the case of 'why' questions about assumptions of theories only by appeal to a more fundamental theory."
I can't say how I agree with you. You have formulated it beautifully.
Dale, you said:
"Science is notoriously bad at answering “why” questions for the assumptions of our fundamental theories."
One of the assumptions of Newton's Mechanics was the assumption of the existence of something like gravity. People asked him: what is gravity and where does it come from...
weirdoguy
On Wikipedia in the Article Four causes you can read:
Aristotle held that there were four kinds of answers to "why" questions (in Physics II, 3, and Metaphysics V, 2): Matter, Form, Agent and End of purpose and of course I did not mean an End of purpose answer with my why-question .
Perok I totally agree with what you said with "It's not as black and white as that." and further. That is also exactly my opinion of how science works.
Perok Your last answer:
Probably the simplest way is to derive the relativistic expressions for energy ...
seems very promising to me. I'm going to take a good look at it. Thanks a lot.
weirdoguy said:
Yes, and that answer leads to other questions of the "why?" type. And at some point, our answer has to be "because that's the way Universe works". That was the point.
Again I say: that is nonsense, because that would mean that we would no longer ask questions and that is the...
BvU said "Ours is not to reason why."
I do not agree with such an answer. If someone asks: why does the moon have different phases then we all know the answer and it is nonsense to say: Ours is not to reason why.