# Tagged Questions

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use ...

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### Finding $\mathbb{E}(X+1)$ and $\mathrm{var}(X+1)$ of a Poisson rnd variable

In this exercise: Let $X$ be a Poisson random variable with parameter $\lambda$ and let $Y=X+1$. Find $\mathbb{E}(Y)$ and $\mathrm{var}(Y)$. I was able to apply the definition of expected value ...
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### Why can strong law of large numbers be applied in this question?

Let $(X_n)_{n\in\mathbb{N}}$ be i.i.d. random variables taking values in the set of natural number $\mathbb{N}$. Assume that $\mathbb{P}(X_1=i)=p_i>0$ for $i\in\mathbb{N}$. Let $D_n$ denote the ...
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### When is a random variable is said to be well-defined?

In the paper On the Bootstrap of the Sample Mean in the Infinite Variance Case by Keith Knight, on page 1170 at the bottom of the page before the theorem, the author mentions that the random variable ...
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### Change in probability complexity when adding 2 “wildcards” (jokers) to a standard 52 card deck

I am wondering what happens to the complexity of probability when "wildcard" conditions are allowed in random card draws. For example, the probabilities of the $5$ card poker hands from a standard ...
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### How to calculate conditional probability with inequality

I know that: $$\displaystyle P(A=x|A+B=y) = \frac{P(A=x \cap A+B=y)}{P(A+B=y)}$$ Assuming $A$ and $B$ are independent, the intersection of the two events can be resolved as ...
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### Simple finding the PDF given function

I am a little confused on how to go about finding the PDF given a condition for a function. So I have the function $$Y(x)=ae^{-bx} \,\,\,\,\,\,\, a,b,x \geq0$$ and I need to find the value for X ...