Is there a two-dimensional random variable $(X,Y)$, whose CDF is continuous, but whose marginal CDFs are discontinuous?  My question differs from  in that a random variable that has a continuous CDF, which is the condition stipulated in my question, is not necessarily a continuous random variable, which is the condition stipulated in the other question. Thus, my question is more general than the other one.
Just need help understanding this question, as I don't really understand what a continuous random vector is. My limited understanding is that a continuous random vector must be completely continuous (so for continuous X and Y this is satisfied) and that to get the probability of the random vector occurring, we double integrate over the supports (of X and Y obviously). My guess is then, that the c.r.v (X,Y) IS a continuous random vector.  Also, what of the converse? If (X,Y) is a continuous random vector, then are X and Y continuous random variables? I also think this is correct, as the continuity of the vector MUST imply the continuity of X and Y, although I'm honestly not sure.  Thanks
How to find out who deleted some data SQL Server My boss had a query from a customer yesterday asking how they could find out who deleted some data in their SQL Server database (it is the express edition if that matters).  I thought this could be found from the transaction log (providing it hadn't been truncated) - is this correct? And if so how do you actually go about finding this information out? How do I get a file extension in PHP? How can I build XML in C#? How can I generate valid XML in C#? How do I locate all files that include specific word as part of name and end with specific extension? How can I convert a node made material into an image texture? I have a sphere having a planet material MADE WITH NODES, and I want to convert this material into an image texture; because this material is made with nodes and only works in Blender, but I want to use in another software. This is my sphere material :   For Example : This is Jupiter :  And this is the texture :  In this case I used a downloaded image for Jupiter to be the material but I want the opposite, I want to change the material to image texture Like The shape of Jupiter texture. Is there anyway in Blender that can achieve my goal ? This is the file with my sphere material .  Textures Needed :  Albedo / Color / Diffuse Normal Map Roughness Glossines  I am using normal nodes and I am not useing the new Principled-shader Reading Excel files from C# A coin is tossed $n$ times. What is the probability of getting odd number of heads?   I started this chapter sometimes ago and faced in front of a tough problem. At first I started considering cases. Case-I : The probability of getting 1 head.Case-II : The probability of getting 3 head and so on. But there are many cases. So how can I solved this . Please help me. Thank you! Don't you think people need to know what they did wrong exactly so they can fix it and get unbanned from asking questions or posting answers? I am interested in how uncertainty can be accounted for when considering the risk of extinction of a species. Forgive me for extending a rather tired thought experiment, but at least it's familiar territory and I hope it illustrates what I am trying to understand.  Let's say that Schrödinger was not satisfied with killing and not killing only one cat, so he went out and collected the last 15 remaining Himalayan Snow-Cats. He put each one in a box with a vial of poison, hammer, and a trigger device for releasing the hammer. Each trigger device has a known probability of releasing the hammer within any given hour, and the poison will take 5 hours to kill a cat (things got a bit trippy when he used radioactive decay, so this time he steers clear of quantum mechanics). After one hour, Schrödinger receives a notice from the ethics board telling him he's nuts and ordering him to release the cats immediately. He pushes a button which opens a cat-flap at the back of each box, thus releasing them all back into the wild. By the time the humane society check the boxes, all the cats have bolted. Before anyone can restrain him, Schrödinger detonates the remaining triggers, so nobody knows how many of the cats were poisoned.  The probability that each of the cats is poisoned is as follows:   0.17 0.46 0.62 0.08 0.40 0.76 0.03 0.47 0.53 0.32 0.21 0.85 0.31 0.38 0.69   After 5 hours have elapsed and all poisoned cats have died, what is the probability that there are:   (A) More than 10 Himalayan Snow-Cats still alive  (B) 10 or less still alive (C) 5 or less still alive (D) 2 or less still alive When is a function too long? Simulating data to fit a mediation model I am interested in finding a procedure to simulate data that are consistent with a specified mediation model.  According to the general linear structural equation model framework for testing mediation models first outlined by  and described elsewhere such as , mediation models for outcome $Y$, mediator $\newcommand{\med}{\rm med} \med$, and predictor $X$ and are governed by the following three regression equations: \begin{align} Y    &amp;= b_{11} + b_{12}X + e_1                \tag{1}  \\ \med &amp;= b_{21} + b_{22}X + e_2                \tag{2}  \\ Y    &amp;= b_{31} + b_{32}X + b_{32} \med + e_3  \tag{3} \end{align} The indirect effect or mediation effect of $X$ on $Y$ through $\med$ can either be defined as $b_{22}b_{32}$ or, equivalently, as $b_{12}-b_{32}$.  Under the old framework of testing for mediation, mediation was established by testing $b_{12}$ in equation 1, $b_{22}$ in equation 2, and $b_{32}$ in equation 3.  So far, I have attempted to simulate values of $\med$ and $Y$ that are consistent with values of the various regression coefficients using rnorm in R, such as the code below:  x   &lt;- rep(c(-.5, .5), 50) med &lt;- 4 + .7 * x + rnorm(100, sd = 1)   # Check the relationship between x and med mod &lt;- lm(med ~ x) summary(mod)  y &lt;- 2.5 + 0 * x + .4 * med + rnorm(100, sd = 1)  # Check the relationships between x, med, and y mod &lt;- lm(y ~ x + med) summary(mod)  # Check the relationship between x and y -- not present mod &lt;- lm(y ~ x) summary(mod)   However, it seems that sequentially generating $\med$ and $Y$ using equations 2 and 3 is not enough, since I am left with no relationship between $X$ and $Y$ in regression equation 1 (which models a simple bivariate relationship between $X$ and $Y$) using this approach.  This is important because one definition of the indirect (i.e., mediation) effect is $b_{12}-b_{32}$, as I describe above.  Can anyone help me find a procedure in R to generate variables $X$, $\med$, and $Y$ that satisfy constraints that I set using equations 1, 2, and 3? Evaluate the integral $\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\,\mathrm dx$. Evaluate the integral $$\int^{\frac{\pi}{2}}_0 \frac{\sin^3x}{\sin^3x+\cos^3x}\, \mathrm dx.$$  How can i evaluate this one? Didn't find any clever substitute and integration by parts doesn't lead anywhere (I think).  Any guidelines please? What are the origins of the word orientated?  As far as I know, the correct spelling is oriented and orientated is not an alternative spelling but an error that is in common use.  Is it for example more commonly used in a certain country or by a certain people? Is there a reason for people choosing to say or write orientated instead of oriented? How can I add "Show desktop" to the GNOME dash or Ubuntu Dock? After seeking clarification about linear model coefficients  I have a follow up question concerning non-signficant (high p value) for coefficients of factor levels.  Example: If my linear model includes a factor with 10 levels, and only 3 of those levels have significant p values associated with them, when using the model to predict Y can I choose to not include the coefficient term if the subject falls in one of the non-signficant level?  More drastically, would it be wrong to lump the 7 non-significant levels into one level and re-analyze? $|f'(x)| \le g(x)$ implies $|f(b) - f(a)| \le \int_a^b g(x) dx$, without assuming $f'$ to be integrable. Can all fundamental forces be fictitious forces? Jumping in an elevator? Messed up Blender models when exporting to Unity3D I have modeled a simple pocket watch in Blender. Every time I import it into Unity3D, regardless of whether I export it from Blender as an FBX or 3ds file, it always comes out missing faces! Why is this happening? I have never had problems importing models into Unity3D like this before.  Blender Screenshot    Unity Screenshots     It seems to me that different faces appear when I rotate it differently. How can I prevent this? Thanks! How to add startup applications in lubuntu? Is there a 'Startup applications' app for lubuntu? Or how do I add apps to startup? I attempted a tutorial to add entries to ~/.config/autostart, but it did not work. Isn't there an easy way? Any ideas please?