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Results tagged with Search options questions only user 30438
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Probability density function (PDF) of a continuous random variable gives the relative probability for each of its possible values. Use this tag for discrete probability mass functions (PMFs) too.

If $f(x,y)=2x , 0\leq x\leq 1 ,0\leq y\leq 1$, find $P(Y < e^{-X} \cap X > Y)$ Given X and Y have joint distribution. Here is my approach: $$P(Y < e^{-X} \cap X > Y) = 1- P(Y > e^{-X} \cap X > Y) … asked Oct 8 '13 by user30438 2answers Let U,V,W are independent random variables with \mathrm{Uniform}(0,1) distribution. I am trying to find the probability that Ux^{2}+Vx+W has real roots, that is, P(V^{2}-4UW> 0) I have solved … asked Oct 14 '13 by user30438 1answer (-(1-y)^\frac {1}{2} < X < (1-y)]$$ From here, I can get $F_{Y}(y)$, and differentiating it will give me $f_{x}(x)$. But the answer I am getting for pdf is not the desired answer. Am I doing anything wrong? Thanks for your help. …
Suppose that $X$, $Y$ and $Z$ are $\text{i.i.d.} \sim \text{Uniform}(0,1)$. Let $t > 0$ be a ﬁxed constant. (i) Compute $P(X/Y \leq t)$ (ii) Compute $P(XY \leq t)$ (iii) Compute $P(XY/Z \leq t)$ …
Trying to prove that this doesn't belong to exponential family. $f(y|a)=4\frac{(y+a)}{(1+4a)} ; 0 < y < 1 , a>0$ Here is my approach: $$f(y|a) = 4(y+a)e^{-log(1+4a)}$$ $$f(y|a) = (4y)(1+\frac{a}{y … asked Oct 1 '13 by user30438 1answer }) \$$ The issue I have is to get pdf $f_{Y}(y)$ for $$-\infty < y < 0$$ of function $$\frac{1}{2}e^{-|x|}$$ pdf =  \frac{1}{3} (y^{-\frac{2}{3}})[\frac {1}2 e^{-y^\frac{1}{3}} + \frac{1}{2}e^{-y^\frac …
Given: $f_{Y_{(1)}}(y) = nbe^{-nb(y-a)}$, where $b> 0$ and $y \geq a$. Show that as $n \rightarrow\infty$, $Y_{(1)}$ converges to $a$ in probability. I have calculated $E[Y_{(1)}] = \frac{1}{nb} + a … asked Nov 3 '13 by user30438 0answers Given$ Y_1, Y_2..Y_n$are iid from a distribution with pmf,$f(y) = a^{2}$for$y=0$,$f(y) = 2a(1-a)$for$y=1$,$f(y) = (1-a)^{2}$for$y=2$, where$0<a<1$. For large n, calculate the appro … asked Nov 2 '13 by user30438 0answers Suppose$X1,..,X4$be iid from pdf$f(x|\theta)=\frac{1}{\theta}$,for$0<x<\theta$. The prior distribution is$\pi(\theta)=\frac{2}{\theta^3}$, for$\theta>1$I have to obtain: a)posterior … distribution of$\theta$given$Y$, where$Y = max(X1,...,X4)$. b)point estimate of$\theta$based on median of posterior. My work a) Starting with pdf of$Y$,$f_{X(4)}(y)=\frac{4y^3}{\theta^4 …