Stefan Hansen
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 17h comment Find the density function from a joint density function Independence implies $\mathbb{E}[XZ]=\mathbb{E}[X]\mathbb{E}[Z]$ but not the other way around. Apr 20 revised Are Monotone functions Borel Measurable? rolled back to a previous revision Mar 31 reviewed Reject how do i calculate the threshold value of the following problem? Mar 29 awarded Necromancer Mar 22 answered Independence of random variable and random vector implies conditional independence Mar 15 comment CDF expected value when Y=X^2 If X=0 then what is Y? Mar 7 comment Finite group with at least 3 generators? If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. - From Review Mar 2 awarded Nice Answer Feb 29 comment Is $f$ a probability density function? I would start by taking a look in my textbook if I didn't know the precise definition of a probability density function. Feb 29 comment Is $f$ a probability density function? @Qwerty: That depends on what your definition of '$f$ being a probability density function of $X$' is. Surely, this must be stated in the textbook or lecture notes you are following. Feb 29 comment Is $f$ a probability density function? @Qwerty: That definition still doesn't depend on $X$, so surely this can't be the definition of '$f$ being a probability density function of $X$'. Feb 29 comment Is $f$ a probability density function? @Qwerty: That definition doesn't involve X. Feb 25 comment Is $f$ a probability density function? You're asked to prove that "f is if and only if f satisfies ", so surely you must be given the definition of in order for this to make sense. Feb 24 awarded Yearling Feb 19 comment Proof of an algebra (measure theory) Induction in the number of sets would do it. Feb 12 comment Independence of two non-negative integer valued random variables Hint: $\{X\leqslant a\}=\bigcup\limits_{j=0}^{\lfloor a\rfloor} \{X=j\}$. Feb 10 awarded Nice Answer Feb 10 comment Given three independent events $A,B,C$, is $I_A+2I_B$ independent of $I_C$? If you want to argue in terms of sigma-algebras, then just note that by assumption $\sigma(I_C)$ is independent of $\sigma(I_A,I_B)$. Then, since $\sigma(I_A+2I_B)\subseteq\sigma(I_A,I_B)$, we also have $\sigma(I_C)$ is independent of $\sigma(I_A+2I_B)$. Feb 9 comment Find the distribution of $Y = -\log (1-X)$ given that $X\sim U(0,1)$. What have you tried yourself? Please explain. Feb 2 answered Expectation of min(X,1)