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2d
comment Can a set in $\mathbb{R}^2$ be closed but unbounded?
$\mathbb{N}^2$ for example.
Aug
13
comment If $ P(A) = 0 $ is $ A $ a null event?
A null set in general is a set that is contained in a measurable set with probability (or measure) zero. The null set itself need not be measurable. But I think it's unclear whether "null event" in the question refers to a null set or the empty set.
Aug
13
comment If $ P(A) = 0 $ is $ A $ a null event?
That depends on whether the term "null event" refers to the empty set or to a null set.
Aug
12
reviewed Close Proof of finite expectation of renewal process (2)
Aug
12
revised Proof of Double Expectation of a Conditional Expectation
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Aug
12
comment Proof of Double Expectation of a Conditional Expectation
You can, but that requires a different, more general definition of the conditional expectation ${\rm E}[Y\mid X]$ (one not using densities, of course). Are you familiar with such?
Aug
12
answered Proof of Double Expectation of a Conditional Expectation
Aug
11
comment Do we need $\mu, \nu$ to be $\sigma$-finite to show $\int fg \ d(\mu \otimes \nu) = \int f \ d\mu \int g \ d\nu$?
$\mu\otimes\nu$ is only well-defined when $\mu$ and $\nu$ are $\sigma$-finite.
Aug
11
comment Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?
You replaced too much. $Q_n$ is defined on $F_n$, i.e. $Q_n$ takes a set from $F_n$, not a function or random variable $\mathbf{1}_A$ as you wrote. I've edited accordingly.
Aug
11
revised Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?
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Aug
11
answered Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?
Aug
11
comment Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?
Then $L_n A_n$ doesn't make sense. You probably want to define $Q_n(A)={\rm E}[L_n\mathbf{1}_A]$ for $A\in F_n$, where $\mathbf{1}$ is the indicator function.
Aug
11
comment Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?
So there are two sequences, $(A_n)$ and $(L_n)$? Then how is $Q_n(A_n)$ defined? If you're supposed to show that it is a probability measure, then you must define what it does to a set.
Aug
11
comment Is $Q_n(A_n)=E(L_n A_n)$ a probability measure?
What is $A_n $?
Aug
10
comment The general form of a measurable set in a product measurable space
No. Yes, take $X\times Y$. No. Yes, take $\varnothing\times\varnothing$.
Aug
9
reviewed Looks OK want to prove exponential identity with complex numbers
Aug
8
comment Probability Density Function for Discrete and Continuous Random Variables.
Not sure what you mean by "easy", but the pdf of the (standard) uniform distribution is quite easy to plot. It's 1 on the interval [0,1] and zero outside.
Aug
8
comment Probability Density Function for Discrete and Continuous Random Variables.
@Kraken: The area below the pdf from $a$ to $b$ is exactly $P(a\leq X\leq b)$. So it signifies where the random variable has its probability mass.
Aug
8
comment Probability Density Function for Discrete and Continuous Random Variables.
Yes, he most likely did plot the pdf (probability density function) which is not the point probability. However, if $f$ is the pdf of a random variable $X$, then $P(x\leq X\leq x+\mathrm{d} x)\approx f(x) \mathrm{d}x$ for small $\mathrm{d}x$.
Aug
8
comment Probability to guess at least one answer correctly
What is the probability of not answering any of the three problems correctly?