$X\sim R(0,1)$ and $Y\sim R(0,1)$ (X and Y are uniformly distributed on the interval $[0,1])$  I need to find the density function of W when $W=X\cdot Y$   Can anyone help me?
Say $X_1, X_2, \ldots, X_n$ are independent and identically distributed uniform random variables on the interval $(0,1)$.  What is the product distribution of two of such random variables, e.g., $Z_2 = X_1 \cdot X_2$?  What if there are 3; $Z_3 = X_1 \cdot X_2 \cdot X_3$?  What if there are $n$ of such uniform variables? $Z_n = X_1 \cdot X_2 \cdot \ldots \cdot X_n$?
How can I count unique selections from multiple selections in a drop down list (Excel) I would like to count the number of unique selections from a column that contains multiple selections from a drop down list.  For example, column B3 contains,     Monday, Tuesday, Wednesday   The count function returns a value of 1 instead of 3 - is there any way to count the three days distinctly? Thank you!  Multiple selections from a drop down list was made possible using the VBA code from: In my passport, my name is Firstname middlename1 middlename2 lastname, and in the ticket is LASTNAME/FIRSTNAME MR.  Will be a problem? I'll travel from Brazil to Bali, Indonesia and according to the agency I bought the ticket from, there's no problem and it's common.  The airline is Qatar Airlines and I have looked , which says that the passenger name can't be changed after the booking has finished.  But I don't know if it is a problem. I'd like to know if there is any alternative to Deep Freeze for Linux that still under development, because I've read some things on the internet and looks like the same company which developed Deep Freeze had a Linux version of it, but the project was discontinued. Why $\sqrt{-1 \times -1} \neq \sqrt{-1}^2$? We know $$i^2=-1 $$then why does this happen? $$ i^2 = \sqrt{-1}\times\sqrt{-1} $$ $$ =\sqrt{-1\times-1} $$ $$ =\sqrt{1} $$ $$ = 1 $$  EDIT: I see this has been dealt with before but at least with  I'm not making the fundamental mistake of assuming an incorrect definition of $i^2$. Why use a ReentrantLock if one can use synchronized(this)? Constant term in Lagrangian Why can we always drop any constant term in a Lagrangian density in quantum field theory?  This issue is somehow related to the constant term being some kind of cosmological constant.  Can you please explain this issue? Should I use the past tense with did? Should I use the past tense with did? For example, I was to say:     The important question is: Did they knew what it means or not?   Or should I say:     The important question is: Did they know what it means or not?   In other words: Should I use past tense with did?  I looked at this:    but it didn't really answer my question. I have absolutely no experience with Linux, and I desperately need to get my computer back up and running again with Windows.  How do I remove Ubuntu and reinstall Windows?    Editor's note: many of the answers are about removing Ubuntu from dual-boot but keeping Windows (which is a bit complicated), while other answers are about removing Ubuntu from single-boot (which is easy: basically just format the disk while installing Windows). The question as written is ambiguous between dual-boot or single-boot. Suppose that sequences of real numbers satisfy:  \begin{align*}   a_n &amp;= \sum\limits_{r=0}^n \binom{n}{r} b_r \\ \end{align*}  Prove that:  \begin{align*}   (-1)^n b_n &amp;= \sum\limits_{s=0}^n \binom{n}{s} (-1)^s a_s \\ \end{align*}  My work:  The $n=0$ case:  \begin{align*}   a_0 &amp;= b_0 \\   b_0 &amp;= a_0 \\ \end{align*}  Then $n=1$ case:  \begin{align*}   a_1 &amp;= \binom{1}{0} b_0 + \binom{1}{1} b_1 = b_0 + b_1 \\   -b_1 &amp;= \binom{1}{0} a_0 - \binom{1}{1} a_1 = a_0 - a_1 \\   b_1 &amp;= a_1 - a_0 = b_0 + b_1 - a_0 = b_1 \\ \end{align*}  The inductive step:  \begin{align*}   (-1)^{n+1} b_{n+1} &amp;= \sum\limits_{s=0}^{n+1} \binom{n+1}{s} (-1)^s a_s \\ \end{align*}  I'm not sure where to go from here. I tried substituting $a_s$ into that last equation and it didn't help. Any ideas? I'm using pdflatex, and use \includegraphics to include content of figures from PDF. PDF are exported from InkScape.  \begin{figure} [!h]     \centering     \includegraphics[height=3cm]{fig/SUSAN.pdf} \end{figure}   Included PDF or source SVG has same colors. Green has always RGB value (0, 255, 0). Problem occurs when I include this files from LaTeX. In output PDF on some pages colorspace is darker. Even same image on other page has different colourity.  My PDF  . As you can see on page 7 (11 in PDF) USAN areas are bright green, but then on page 5 (9 in PDF) are green points on corners more darker. I'm stuck in a teleporting loop. What can I do? Passing custom string into a Salesforce email template. I just stumbled upon a :     My wife and I's seafood collaboration dinner. How does it look?   Sure enough, the top comment immediately points out that it should be "my wife's and my". However, a cross-post to the Grammar subreddit produced :     It's fine as it is written. "my wife and I" is a noun phrase, functioning as a subjective pronoun in the singular and made possessive with the apostrophe. It is exactly the same as "our".      It seems weird because you would never use "I's" on its own but it is not on its own here - it is part of a noun phrase.   That's a rather intriguing argument. Does it hold any water? How to get correlation between two categorical variable and a categorical variable and continuous variable? I am building a regression model and I need to calculate the below to check for correlations   Correlation between 2 Multi level categorical variables Correlation between a Multi level categorical variable and continuous variable  VIF(variance inflation factor) for a Multi level categorical variables   I believe its wrong to use Pearson correlation coefficient for the above scenarios because Pearson only works for 2 continuous variables.   Please answer the below questions   Which correlation coefficient works best for the above cases ?  VIF calculation only works for continuous data so what is the alternative?  What are the assumptions I need to check before I use the correlation coefficient you suggest?  How to implement them in SAS &amp; R? Is there a way to make sure that a deleted file can not be recovered?   As you know, deleting a file by pressing shift-del or using trash doesn't mean that file is gone forever. It resides somewhere in the computer.  In day to day life, law enforcement or thieves use recovery programs to reveal our private data or something else.   They can recover all data that resides on hard disk, in RAM, and even USB.  To protect us from these people, what should one do? Which program should one use?  Note: I don't want an answer like first use a recovery program then erase that file with shred. With just one program, I want to erase all unused/deleted files on my computer. Hyperref - Token not allowed Possible Duplicate:          The following code:  \subsection{The classes $\mathcal{L}(\gamma)$}   generates the errors:  Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `\gamma' on input line 1938.   Package hyperref Warning: Token not allowed in a PDF string (PDFDocEncoding): (hyperref)                removing `math shift' on input line 1938.   What do I have to do to keep \gamma in the subsection, so that it is also listed in the table of contents? Intersection of the $p$-sylow and $q$-sylow subgroups of group $G$ Reading order for Dragonlance? Prove that the product of two continuous functions is continuous Finding all software packages in Debian that provide a particular alternative The Debian distribution has the . From the Wiki:     The Debian alternatives system creates a way for several programs that   fulfill the same or similar functions to be listed as alternative   implementations that are installed simultaneously but with one   particular implementation designated as the default. For example many   systems have several text editors installed at the same time. The vi   program is a classic example of an editor that has many   implementations such as nvi, elvis, vim, etc. but which one should be   designated as the default?   In general, there are multiple packages in Debian that provide a particular alternative. How does one obtain a complete list of all such packages that exist in the Debian repositories? Let us use the vi alternative as an example.  NOTE: Doing such a query against the list of installed packages is easy, but that is not what this question asks.