Distribution (mathematics) Puns

I know that expected value is equal to Σ X ∙ P(X), but I'm not sure what to substitute for X.I also know that P(X=k) = 1/n (for integers 1 ≤ k ≤ n) if that is any help for this question.

I don't even know if you use that formula for this question either.

Question: A random variable X is chosen from a uniform distribution with values: 1, 2, 3, ..., n. What is the expected value E(X)?

https://docs.google.com/forms/d/e/1FAIpQLSeU0R5N_y28RpXjJuKry8TzvwqlPCoqySsHdzah8mqd0OqyrQ/viewform

Survey regarding IQ and test results, any help with responses would be greatly appreciated :)

According to a professor of mine in an upper level undergraduate mathematics course, they received an email that instructed them to not typically release the distribution of grades on exams. Apparently the department has received numerous requests for grades to be curved in multiple courses because of poor performance across the board. Has anyone else heard of this?

More so, is it not legitimate to look for curves when the school is failing students across the board in multiple courses? Isn't hiding the distribution of grades a shady underhanded solution to the departments problem, as opposed to recognizing failures in the online modality?

Obviously I imagine this is the most biased place I could ask this question, but I just wanted to see other students thoughts.

So basically, most of my question is in the title. I'm working on an undergrad project on modelling, which personally, I thought would be super ODE/PDE focused, and I didn't realize I'd really be working with probability distributions as well, and even that, to a large extent. Personally, I'd always been a little bad at working with probability (at least in my intro level classes), so I was a little dumbfounded when I found out what I had to do, but I guess I'll just stick with it and keep working to see where I get.

Anyway, basically, what I'm doing is modelling the spread of Covid in my country, and I was studying papers from other countries (like new zealand, ukraine, china etc.), and I noticed a lot of them used probability distributions. And specifically, what I saw most up until now were the Weibull, gamma and lognormal distributions.

What I want to know is; how important are distributions to modelling the spread of something? Why do we use that specifically when you can use a differential equation system to model it as well? And also, what is special about the distributions that I've mentioned above that makes them useful for this situation in particular? Are there any others that are used as well? How would I know which ones are appropriate for what I'm looking at?

I apologize for the extremely long list of questions, and I'd really appreciate if anyone could let me know the answers to them. Thank you all in advance!

I was reading about math prodigy Terence Tao's life and learned that he "taught himself to read before the age of two," as well as other surprising feats [1] such as scoring a 175+ IQ at age 6.

The way I see it, if being a math prodigy like Tao does not require being born inherently gifted, then we should theoretically be able to "teach" children to be math prodigies. However, it seems to be the case that certain rare genetics are necessary to give a child the potential to be a math prodigy, so I doubt that this is possible.

As for those falling "on the extreme right end of the mathematical ability distribution," it seems to me that we should expect genetics to be necessary at these extraordinarily high degrees of ability, just as we see with competitive professional sports (certain genetic traits, such as height, are more or less valuable for specific sports).

Am I misunderstanding something? Is my intuition incorrect?

[1] Exceptionally Gifted Children", 2nd edition, by Miraca Gross ​

Having some trouble with this one (Assumed I would use the pidgeonhole principle but it didn't work)

In how many ways can you distribute 13 apples and 7 pears to 8 children, if each child gets one apple?

I ASSUME the question means "at least on apple"

Thanks!

The question linked below has got me stumped! I thought of substituting z or looking at how the problem relates to the normal distribution function, but I can't see how to do this. Help, please?

Question here

I read sources that talk about noise levels at different ISO values. I understand how a higher number for dynamic range of digital cameras means you could in theory go further below middle grey (or the highlight clip point) before it becomes unacceptable. I noticed that both quantization techniques for noise and dynamic range can be cheated through in camera software based suppression. It does not fix the blocking of details caused by chroma noise (it's an artifact caused by sensor noise prior to the A/D conversion). I know noise is a random distribution.

Having said that, for comparison, adding 1 candle flame to 1000 flames in the same scene will not be perceived as obvious compared to adding 1 candle flame to 9 flames. It's part of Weber's law. I know (1000+1)/1000 yields 1.001 while (9+1)/1 yields 1.11111

I know logarithms are used for obtaining fair comparisons. I noticed that the RMS level used for quantifying graininess for film uses a lower number for smaller distribution. It means a lower number means the random distribution is harder for humans to detect (there're other factors). This is something that makes sense.

Why does the SNR commonly used for measuring noise levels follow a relationship where a higher number means the perceived distribution from noise is not as noticeable in a fair comparison? How is that not mathematically backwards? Why does the dB have it that way to begin with?

Since Wargaming has announced the lootbox probabilities, I wanted to make a post about how the mathematics of lootboxes work. To simplify I will focus exclusively on the probability p of getting tier 8 tanks if you buy n lootboxes.

We call each time you open a lootbox a "trial". In each trial we will simplify by assuming that there are only two outcomes or "events" of interest. Either you get a tier 8 premium or not.

We also assume that p is constant - it does not change over time and that the trials are independent.

Statistical theory tells us that we can evaluate such probabilities using the binomial distribution. WG says the chance of a tier 8 is 2.4%. Thus p=.024.

You can use this handy binomial distribution calculator to evaluate the probabilities involved.

For instance, using the calculator, we can see that in order to have a >50% chance of getting a tier 8 tank, you must buy >29 boxes. In other words, exactly 29 boxes, the probability of getting at least one tier 8 (i.e. 1 or more tier 8s) is ~50%.

There is also a new mechanic this year: if after 49 boxes you haven't gotten a tier 8, you are guaranteed to get one on the 50th. Each time you get a tier 8 the counter resets.

The probability of going 49 boxes without a tier 8 is ~30%.

For reference:

I don't remember how to solve normal distribution questions by hand and I don't know what to use to do so.

What and where can I find a resource that teaches me this?

Also can you give solve P(37 < X < 40) if mean is 37 and the standard deviation is 7 as an example?

Thanks!

I just saw the post where the karma earned by users on the subreddit during the previous four weeks was posted. When I looked at the data, I observed that so many people have earned ~ 10k karma. Then I looked at my karma, a mere 695. I wanted to find out where I lie so I decided to run a small data analysis. I found the mathematical distribution of the karma of various users on this subreddit (having karma >0) and also found other other properties.

Normalized probability distribution of Karma

Same plot with a log scale for karma

Normalized probability density for Karma (log scale)

This is the distribution of karma, but moon distribution for a given month is directly proportional to the karma earned (with at 15k cap) so these distributions will be similar.

Other properties of the Karma data

# samples: ~50k

mean = 128.4

50 percentile = 12

75 percentile = 48

95 percentile = 479.45

So if you earned more than 48 karma in the group, you are in the top 25 % for this month. If you earned more than 480, you are in top 5 %. Many people (50% of the users who earned more than 1 karma) have less than 12 karma.

Let me know if you want me to add any other analysis for this data.

EDIT: If you earned more than 2124 karma then you are in the top 1 percent.

Playing with Maths after a long time. Basically it started with the Q: What is the Total income distribution as a function of no of coin tosses.

Given that for everytime it's head I get a reward of R. The probability of getting a head is p.

In this, I figured out that for i successes in n tosses, the (prob)*(income) is C(n,i)*p^i * (1-p)^(n-i) * R^i R.i (binomial dist)

Summing this: T(n) becomes ((p.R + 1-p)^n = (p(R-1) + 1)^n)

T(n) = summation of [C(n,i) * p^i * (1-p)^(n-i) * R.i]

I know it should add upto something, couldn't remember? [It's been a while I've left school]

(Is this expression correct? The trailing + 1 looks a bit odd to me. Is it because the game didn't have any punishment when it's tails, in which case T(n) = (p.R - (1-p)Q)^n where Q is the punishment.)

Now, that '1' is rightfully gone- which was one of my main itch

.

Now I tried to increase the dimensions in the problem(not exactly higher dim version of the same problem, though). How do I solve it(orig prob above)?

.

>>>> The problem yet to be solved is as follows:<<<

T(n)= Expected value of Total Score after n roll of dices.

1. Total Score is simply addition of individual scores from each throws. Nothing fancy.

2. Dice is fair. Nothing fancy.

How is the T(n) distributed over n? <<<< Main Q to be answered

.

I know it has to do with the (i,j,k,l,m,q)th term of expansion (1 + 2 + 3 + 4 + 5 + 6)^n

.

Now, I wonder:

What are these sets of problems? Is there any sub-branch of mathematics dealing with these?

Also, is there any simpler way of expressing (i,j,k,l,m,q...)th term of (what I hope is )higher dimensional version of Binomial Distribution?

What if the dice becomes unfair, OR instead of rolling a dice it's picking out a number randomly from 1 to m instead of just 1 to 6?

.

.

PS:

Sorry if I didn't put it clearly, I was up all night wondering about this randomly for no apparent reason.

Sorry again, as I know how frustrating an ill-worded problem can be.

Ok, so I have experience in statistics but I am no expert.

I may be wrong, but I believe that the normal distribution can only perfectly describe itself, that is, there is no natural random variable out there that has a distribution that is exactly normal. In a sense it is just a good (in some cases very good) approximation of the behaviour of many observable natural phenomena.

Now, before Gauss, say someone came up with a distribution that had many of the same features:

• symmetrical about its mean
• large amount of points relatively close to the mean.
• continuous i.e. still with the distinctive bell shape.

would this function have been as well received and persisted in modern mathematics? since it also would only perfectly describe itself and be a good approximation for many natural random variables.

Thanks in advance

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I've been programming for years now and I've mostly done iOS development and some backend projects but recently I had a change of heart and really want to focus on distributed computing and blockchain which through reading books contains lots of algorithms. The problem is I barely understand the math I'm looking at online or in books I own.

I haven't touched high school math in years and pretty much forgot everything about it, so I'd like to start over so I can really understand what I'm doing. Where should I start learning? Should I start with Algebra 1 and work my way up through some textbooks I can purchase? I also found this neat site called Brilliant which has a lot of math I can do on it.

Thank you in advanced to anyone that will point me in the right direction! :)

Ben is moving to a new house and realises that the large boxes he packed are too heavy for him to move. Each large box holds 214 more things than a small box. If he divides 1223 large boxes into small ones, how many small boxes does his stuff fit in, assuming his things occupy equal volume? In order to evenly distribute the load, Mike needs to make sure that he places boxes relatively equally in the truck’s 8 sections. How many of the small boxes need to go in each section?

The question:

> An appliances factory producing large industrial fridges carries out a final inspection for > accidental indents incurred during the manufacturing process. The inspectors have > found that these indents appear randomly around the fridge (according to a Poisson >process) with an average of 1.2 indents per fridge. > > &nbsp; > >(a) What is the probability that a fridge will have at least one indent? > > &nbsp; > > > (b) Four of these fridges have been selected at random to ship off to a new butchers shop. > What is the probability that there are no more than 6 indents in total on these four > fridges? > > &nbsp; > > (c) The managers of the appliance factory have told the inspectors to set aside any fridges > with no indents, so that they may be sold at a premium price. In a randomly selected > batch of ten fridges, what is the probability that at least half of them can be sold at the > premium price? You may use your answer to Question 1 rounded to 2 decimal places for > this question.

&nbsp;

I understand the simple "box of apples has on average 2.3 spoiled fruit per box of 30 - find the probability of there being more than 5 in a box", but I am undecided on where to start with this one. May I please have some guidance? Thank you.