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Results tagged with self-study
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user 102399
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
votes
sum of poisson?
You have a series of $n$ random variables $X_{i}$ where:
$$X_{i}\sim POI(\lambda)$$
Define:
$$S=\sum_{i=1}^{n}X_{i}\sim POI(n\lambda)$$
You want to know:
$$\text{Pr}(S>a)$$
Recall that, for suff …
- 2,891
0
votes
Problem about normal distribution
If we assume that the weight of an orange is normally distributed and that the weights of oranges are independent. Let $X$ be the weight of each orange. So:
$$X\sim N(\mu,\sigma^{2})$$
Define $Y$ as …
- 2,891
0
votes
Assumptions for multiplicative tariff in Non-Life Insurance
I believe the underlying motivation for any assumption is to avoid having $v$ parameters in:
$$E[S]=\mu\sum_{l=1}^{v}\chi^{(l)}$$
Thus, a parametric form for $\chi^{(l)}$ is assumed, which is a func …
- 2,891
5
votes
Accepted
If f(x) is given, what would be the distribution of Y = 2X + 1?
You make an early mistake.
$$\begin{align}
F_{Y}(y)&=\text{Pr}(Y\leq y)\\
&=\text{Pr}(2X+1\leq y)\\
&=\text{Pr}(X\leq \tfrac{1}{2}(y-1))\\
&=\int_{1}^{\tfrac{1}{2}(y-1)}f_{X}(u)\,du
\end{align}$$
Ke …
- 2,891
1
vote
Accepted
...Does the new data indicate a departure from previous admission rates?
Just a quick look. Your statistic is:
$$\chi^{2}=\sum_{i=1}^{3}\frac{(O_{i}-E_{i})^{2}}{E_{i}}$$
For $i=\{1,2,3\}$, your values should be:
$$O_{i}=\{329,43,128\}$$
and
$$E_{i}=\{0.6\times 500,0.0 …
- 2,891
1
vote
1
answer
1k
views
Solving log-logistic distribution parameters from moments
Let's say we have a log-logistic random variable $X$ with probability density function:
$$f(x)=\frac{(\beta/\alpha)(x/\alpha)^{\beta-1}}{(1+(x/\alpha)^{\beta})^{2}}$$
where $\alpha>0$, $\beta>0$ and …
- 2,891
8
votes
Distribution of 2X - Y when X and Y are known
There are a few important results that are required here. Based on the provided answer, I think an assumption of the question was that $X$ and $Y$ are independent random variables.
Let's try and start …
- 2,891
1
vote
How to find manually the value of the likelihood function?
So what you have is a logistic regression model, where $\boldsymbol\beta$ are your regression coefficients and $\boldsymbol X$ is your data. Now, the likelihood function for your model is:
$$\prod_{i …
- 2,891
0
votes
Prove dependence of $X \sim N(0,1)$ and $Y = WX$, where $W$ takes value $1$ and $-1$ with P ...
I'll try and guide you to an answer.
We know:
$$X\sim N(0,1)$$
and
$$W=\begin{cases}
\,\,\,\,\,1, & p=0.5\\
-1, & p=0.5\\
\end{cases}$$
We also know that $Y=WX$. So:
$$Y=\begin{cases}
\,\,\,\,\, …
- 2,891
1
vote
Poisson random variable self-study question
Here's my attempt. Let's assume that the number of invitees (excluding you) to the party, $N$, is Poisson distributed with parameter $\lambda$:
$$N\sim \text{POI}(\lambda)$$
Let's further assume tha …
- 2,891
3
votes
Accepted
Independence of Sum and Difference of Random Variables[CSIR-UGC NET]
I think it's option 4.
We know that the following is true:
$\begin{array}{c|c|c|c|c}
X & Y & W=|{X-Y}| & Z=X+Y & p\\
\hline
0 & 0 & 0 & 0 & 0.25\\
1 & 0 & 1 & 1 & 0.25\\
0 & 1 & 1 & 1 & 0.25\\
1 & 1 …
- 2,891
5
votes
Accepted
What operation can we perform to convert an elliptical plot into a circular plot?
Without commenting on whether you are correct, I can tell you the following.
Let $\mathbf{X}$ be a $d$-dimensional random vector:
$$\mathbf{X}=(X_{1},X_{2},\ldots,X_{d})'$$
The joint distribution f …
- 2,891
0
votes
Correlation.. covariance.. I am so lost
Given your (poorly written) question, I can try and gauge what you've asked.
Given the CAPM holds, we know:
$$\begin{align}
E[R_{i}]&=R_{f}+\beta_{i}(E[R_{M}]-R_{f})
\end{align}$$
where $E[R_{i}]$ i …
- 2,891
1
vote
Distribution function of an exponential random variable
You're correct in saying that an exponential random variable, $\text{Exp}(\lambda)$, with mean 2 implies $\lambda=\tfrac{1}{2}$.
As has been stated in the comments, the question is asking you to find …
- 2,891
1
vote
Finding the PDF of Y, where Y = min X
Consider the general case. Assume $X_{1},X_{2},\ldots ,X_{n}$ are IID random variables with cumulative distribution function $F_{X}(x)$ and density $f_{X}(x)$.
The order statistics are:
$$X_{(1)}<X_{ …
- 2,891