Recent questions in Descriptive Statistics

Z-Scores
Answered

doturitip9
2022-07-10

From the table of standard normal, the value z score is only for -3.99 $\le $ $z$ $\le $ 3.99.

Can it be higher than the range? Is there any programme or formula to compute the probability of standard normal distribution for the range outside -3.99 $\le $ $z$ $\le $ 3.99?

Mode
Answered

glitinosim3
2022-07-09

How do i show this? As this is a discrete R.V, can i be allowed to use Calculus?

Mode
Answered

vasorasy8
2022-07-09

How do i show this? As this is a discrete R.V, can i be allowed to use Calculus?

Mode
Answered

Banguizb
2022-07-09

Intuitively, I would like to think that we can simply take the sum of the modes, i.e:

$\mathrm{Mode}(S)=\sum _{n=1}^{N}\mathrm{Mode}({A}_{n})$

However, this seems unlikely, especially as we would expect that $\mathrm{Mode}({A}_{n})$ could potentially be a set of values, rather than a single value.

So I was wondering if we'd be able to relax this condition to state that $\mathrm{Mode}(S)\subseteq \sum _{n=1}^{N}\mathrm{Mode}({A}_{n})$, where we define $\mathrm{Mode}(A)+\mathrm{Mode}(B)$ as the set formed by taking the sum of each element in $\mathrm{Mode}(A)$ with each element in $\mathrm{Mode}(B)$, formally:

$\mathrm{Mode}(S)\subseteq \sum _{n=1}^{N}\mathrm{Mode}({A}_{n})=\{\sum _{n=1}^{N}{x}_{n}:{x}_{i}\in {A}_{i}\}$

This seems to be true, but I was wondering if we could say anything stronger?

Types Of Variables
Answered

glitinosim3
2022-07-09

Mode
Answered

rjawbreakerca
2022-07-09

$2,3,4,5,3,2$

Here 2, 3 both happen to have same maximum frequency and thus we say there are 2 modes... The above is stated similar in case we have 3 modes or multi modes ... So if there are all distinct numbers then we would have each number having the same maximum frequency as 1 ..so we can say all the numbers are modes...for that dataset...But then I have seen on some websites claiming that such data sets have "NO MODE".

Types Of Variables
Answered

myntfalskj4
2022-07-09

Mode
Answered

Araceli Clay
2022-07-08

Mode
Answered

prirodnogbk
2022-07-07

mean: $\gamma -\beta {\mathrm{\Gamma}}_{1}$

median: $\gamma -\beta (ln2{)}^{1/\delta}$

mode: $\gamma -\beta (1-1/\delta {)}^{1/\delta}$

Also given that

${\mathrm{\Gamma}}_{k}=\mathrm{\Gamma}(1+k/\delta )$

$\mathrm{\Gamma}(z)={\int}_{0}^{\mathrm{\infty}}{t}^{z-1}dt$

$-\mathrm{\infty}<x<\gamma ,\beta >0,\gamma >0$

Now I understand how to calculate the mean, mode and median when given a probability density function. However I'm struggling to go backwards. I initially tried to "reverse" the process by differentiating the mean or median however I know this is skipping the substitution over the given limit.

I then looked for patterns with known distributions and realised they are from Weibull distribution however $\gamma -$. Does this mean essentially this is a typical Weibull distribution however shifted by $\gamma $ and therefore the pdf will be $\gamma -Weibullpdf"$

Mode
Answered

spockmonkey40
2022-07-07

$P(y|\theta )=\frac{{\theta}^{y}{e}^{-\theta}}{y!},y=0,1,2,\dots ,\theta >0$

$P(y|\theta )=\frac{{\theta}^{y}{e}^{-\theta}}{y!},y=0,1,2,\dots ,\theta >0$

Mean and variance of $Y$ given $\theta $ are both equal to $\theta $. Assume that $\sum _{i=1}^{n}{y}_{i}>1$.

If we impose the prior $p\propto \frac{1}{\theta}$, then what is the Bayesian posterior mode?

I was able to calculate the likelihood and the posterior, but I'm having trouble calculating the mode so I'm wondering if I got the right posterior:

$P(\theta |y)=likelihood\ast prior$

$P(\theta |y)\propto ({\theta}^{\sum _{i=1}^{n}{y}_{i}}{e}^{-n\theta})({\theta}^{-1})$

$P(\theta |y)\propto {\theta}^{(\sum _{i=1}^{n}{y}_{i})-1}{e}^{-n\theta}$

Z-Scores
Answered

delirija7z
2022-07-07

$P(z=2)$

I think that this is 0, as z-score is the area under the curve and could be found by integrating the PDF over the range. As the range is 0, the area is also zero. Is that correct?

Z-Scores
Answered

vasorasy8
2022-07-06

I know how to find X and z-scores as well as how to plug things into the z-score formula, but I'm not sure how to solve this one. It says to sketch out a distribution table and find where the mean and SD fall on it, but I'm not sure how to do that.

Z-Scores
Answered

kolutastmr
2022-07-06

From the standard deviation formula for a sample proportion, I found that standard deviation is 0.0016. From there, I plugged that into the z-score formula, and got (0.316-0.333)/0.0016 = -10.625. However, a z-score that high baffles me and I cannot imagine getting a z-score that high. Where did I go wrong?

Z-Scores
Answered

Callum Dudley
2022-07-04

${\int}_{\mu -2\sigma}^{\mu +2\sigma}A{e}^{-((x-\mu )/\sigma {)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x=0.95\ast {\int}_{-\mathrm{\infty}}^{+\mathrm{\infty}}A{e}^{-((x-\mu )/\sigma {)}^{2}}\phantom{\rule{thinmathspace}{0ex}}\mathrm{d}x$

Firstly, am I correct in my presumption? and secondly, is there any way to calculate the integral on the left to prove this point mathematically?

Z-Scores
Answered

prirodnogbk
2022-07-02

$z=\frac{x-\mu}{\sigma}$

And then they explain about the $\mu $ and the $\sigma $ in the formula like this:

These are the mean and standard deviation of data containing the value x.

But is that so ? I don't think the mean and standard deviation should contain the value x.

Z-Scores
Answered

Sovardipk
2022-07-01

Z-Scores
Answered

Pattab
2022-07-01

In column b (area between mean and the z) the score is 0.4505 for a z score of 1.65. And in column c the score is .0495 for a z score of 1.65. I hope you guys can help me.

How do I figure out what proportion fall above 1.65?

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