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Results tagged with Search options questions only user 30438

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.

2
votes
1answer
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: $$ P(Y < e^{-X} \cap X > Y) = 1- P(Y > e^{-X} \cap X > Y) …
asked Oct 8 '13 by user30438
1
vote
2answers
Let $U,V,W$ are independent random variables with $\mathrm{Uniform}(0,1)$ distribution. I am trying to find the probability that $Ux^{2}+Vx+W$ has real roots, that is, $P(V^{2}-4UW> 0)$ I have solved …
asked Oct 14 '13 by user30438
3
votes
1answer
(-(1-y)^\frac {1}{2} < X < (1-y)] $$ 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. …
asked Sep 22 '13 by user30438
1
vote
0answers
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)$ …
asked Oct 12 '13 by user30438
8
votes
2answers
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: $$f(y|a) = 4(y+a)e^{-log(1+4a)}$$ $$f(y|a) = (4y)(1+\frac{a}{y …
asked Oct 1 '13 by user30438
2
votes
1answer
}) \ $$ 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 …
asked Sep 22 '13 by user30438
3
votes
2answers
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
1
vote
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
2
votes
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 …
asked Nov 20 '13 by user30438