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Results tagged with self-study
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user 128502
A routine exercise designed to test one's knowledge; often from a textbook, course, or test used for a class or self-study. This community's policy is to "provide helpful hints" for such questions rather than complete answers.
0
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58
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Finding power of the given test
Given that $X$ is a single observation from $f(x;\theta)=(2\theta x+1-\theta)I_{[0,1]}(x)$ where $-1\leq \theta \leq 1.$
The objective is to test the hypothesis $H_0:\theta\leq0$ Vs $H_1:\theta>0$ wh …
- 605
1
vote
1
answer
36
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Finding given probability
We are given a sample mean $\bar x=15$, standard deviation $s.d=9$. The problem is to find the percentage of data lies between $6$ and $24$ assuming that the data distribution if fairly symmetric. (Op …
- 605
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vote
1
answer
110
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Finding measure of dispersion
Given a data set as follows:
$$\begin{array}{crrrrrrrr}
Classes: & Less\:than\:20 & 20-30 & 30-40 & 40-50 & 50-60 \\
frequency: & 30 & 20 & 15 & 10 & 5
\end{array}$$
The objective is to find …
- 605
6
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4
answers
815
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Proving $P(|X+Y|\leq 2|X|) > \dfrac{1}{2}$
We are given independent and identically distributed random variables $X,Y$ with probability density function $f(\cdot)$ that is symmetrical about $0$.
We need to prove that $P(|X+Y|\leq 2|X|) > \dfr …
- 605
2
votes
1
answer
2k
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Given arithmetic mean and standard deviation for a frequency distribution, the actual class ...
The Text I am reading has a question that goes like this :
Explain clearly the ideas implied in using arbitrary working origin and scale for the calculation of arithmetic mean and standard deviation …
- 605
-1
votes
2
answers
247
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Monte-Carlo simulation
We're asked to find a monte-carlo estimate for : $$ \theta\:=\: \int^1_0 (e^x -1)dx$$
No further info is provided. And I have no idea how to proceed.
What I know is , if we are required to estimate …
- 605
1
vote
1
answer
960
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Maximum likelihood estimation for $\alpha$ with population pdf $f(x;\alpha)=\frac{2}{\alpha^...
A sample of size two is taken from the distribution $ f(x;\alpha)=\frac{2}{\alpha^2}(\alpha-x)I_{(0,\alpha)}(x)$. We need to find the maximum likelihood estimator for $\alpha$.
The likelihood functio …
- 605
4
votes
2
answers
98
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Proving $P(X=Y)=1$ given that $E(Y|X)=X$ and $E(X|Y)=Y$
It's a Prove/Disprove question.
Given $\mathrm{E}(Y|X)=X$ and $\mathrm{E}(X|Y)=Y$ and both $\mathrm{E}(X^2)$ and $\mathrm{E}(Y^2)$ are finite, then $$P(X=Y)=1$$
If we somehow get $\mathrm{Var}(X …
- 605
6
votes
2
answers
2k
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Inequality involving joint cumulative and marginal distributions
We need to establish the given inequality : $$F_X(x) + F_Y(y) - 1 \leq F_{X,Y}(x,y) \leq \sqrt{F_X(x) F_Y(y)}$$ where $X$ and $Y$ are any random variables.
First I tried the R.H.S :
I started working …
- 605