# Tagged Questions

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### Throwing darts at dartboard (cumulative distribution function)

Suppose there is a target shooting game on circle of radius $3$. Think of the result of the shooting as a random experiment, for simplicity, we suppose the hit will always impact on the circle of ...
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### $U\sim \mathcal U(0,a)\overset{?}{\implies}U-\lfloor U \rfloor \sim \mathcal U (0,a-\lfloor a \rfloor$)

Suppose $U\sim \mathcal U(0,a)$ for some $a>0$. Is it true that $U-\lfloor U \rfloor \sim \mathcal U (0,a-\lfloor a \rfloor$)? How can I prove this? If $a\in \mathbb N$ then the following ...
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### Say (X,Y) has the distribution on the area shown below find P(X>1|Y=1/2) [closed]

Say (X,Y) has the distribution on the area shown below, find P(X>1|Y=1/2)![enter image description here][1]
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### uniform distribution over disk

Given two independent random variables $A$ uniform on $[0,1]$ and $B$ uniform on $[0,2\pi]$. Obtain the joint pdf, tranform to the disk, if necessary modify to obtain the uniform pdf over the disk. ...
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### Expectation of $\frac{1}{X+1}$ for a geometric random variable

I am confused over $E(\frac{1}{1+X})$ where $X$ is geometric distribution with parameter $p$. The book wants me to prove that $E(\frac{1}{1+X})=log((1-p)^{\frac{p}{p-1}})$ Here's what I did. ...
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### Presenting a multinomial dstribution as some function of underlying binomials

I have a multinomial distribution, which arises, let's say, for the sake of clarity, from $N$ rolls of unfair $S$ sided dice and labels on the sides are non-integer. I know the probability for each ...