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Jan
27
comment cumulants and infinite divisibility
@A.S. Thank you. I have applied the correction.
Jan
27
revised cumulants and infinite divisibility
added 12 characters in body
Jan
24
answered Integral $\int_0^{\pi/2} \sin(ax)\cos(x)\,dx$
Jan
21
comment Oscillatory integral giving me the willies
@Brightsun thanks for that. Adjusted
Jan
21
revised Oscillatory integral giving me the willies
added 44 characters in body; added 1 character in body
Jan
11
revised Proof convexity of Logarithmic function
added 10 characters in body
Jan
11
comment Proof convexity of Logarithmic function
$f(t)$ is twice differentiable for $t > 0$, so you could check the appropriate criterion, but I am afraid it is concave, rather than convex.
Dec
18
awarded  Enlightened
Dec
18
awarded  Nice Answer
Dec
17
awarded  Nice Answer
Dec
7
answered Conditional expectation for $2X+3 \mid Y$
Nov
13
awarded  Good Answer
Nov
11
comment Prove elementarily that $\sqrt[n+1] {(n+1)!} - \sqrt[n] {n!}$ is strictly decreasing
@0.5772156649... There were 2 bounties awarded, by different users.
Nov
5
answered Exponential integration involving polynomial
Oct
22
awarded  Nice Answer
Oct
18
comment Conditional Probability for Exponential Random Variables (Density Function and Distribution Function)
@SmileySam we started with distribution of $X/Y\mid Y$ , and distribution of $Y$, and derived the joint distributions of $(Y-X, Y)$, which is what converse part asked, did it not?
Oct
15
comment Conditional Probability for Exponential Random Variables (Density Function and Distribution Function)
We have shown that $X \mid Y$ is uniform on interval $(0,Y)$, hence $U = \frac{X}{Y} \mid Y$ is standard uniform and is independent on $Y$. Therefore $X \mid Y = U Y \mid Y$, i.e. $X = U Y$.
Oct
15
comment Conditional Probability for Exponential Random Variables (Density Function and Distribution Function)
Because we showed that $X \mid Y$ is uniform, right? That means that $X$ and $U Y$ are equal in law.
Oct
14
answered Conditional Probability for Exponential Random Variables (Density Function and Distribution Function)
Oct
13
awarded  Nice Answer