Probability and Statistics

[errant rose]

1. Ask your question and show the work you've done so far. If you've posted a screenshot of a question, specify which part you need help with.
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[upbeat parcel]

What are you having trouble with?

[fallow tusk]

Everything really, I wasn't introduced to the unit so I just need some guidance through this work

[upbeat parcel]

Hm... Well, it would be better to at least read on the definitions of all the terms in your textbook.

[fallow tusk]

Thats the thing though😭 I don't really have any textbooks except for any online resources I can find

[upbeat parcel]

Wait, you study without a textbook? That's weird...

Hm. Hold on.

[upbeat parcel]

Well, I learned statistics by Gnedenko and Chistyakov. It's been a while, though...
Both are available in Russian, and I think Gnedenko should be available in English, too. Gnedenko is also definitely available on Libgen.

[fallow tusk]

Yeah im doing online school right now and they just give you the material in Zoom meetings, I havent been present to those because ive been sick.

[upbeat parcel]

Oh, I see... Hope you get better soon!

[fallow tusk]

It's all good, I'm feeling better now, do you think you can still help me witht hese problems though?

[upbeat parcel]

Well, let me remind you the definitions.
Sample mean X̅ is the arithmetic mean of all the observed values. In other words, it's the sum of values divided by their amount.
Sample median median(X) is such a value that the amount of values smaller than it is the same as the amount of values larger than it. In other words, if you order the values, it will be in the middle. If there is an even number of values, you find it by taking the mean of the middle two values.
Range R(X) is the difference between maximum and minimum values.
Sample variance S^2 (X) can be calculated using the formula on the picture: it's the sum of squared differences of observed values and the mean divided by the number of values minus one. Sample standard deviation S(X) is just the square root of sample variance. That's why you're given a table with differences and squared differences, so you can calculate it step by step.

As for properties:

1. Sample mean is linear: a̅X̅ ̅+̅ ̅b̅ = aX̅ + b.
2. Sample variance isn't linear, but still has a similar property: S^2 (aX + b) = a^2 S^2 (X)

I assume you can't use them in exercises (b) and (c) directly, but you can use them afterwards to check the result.

[fallow tusk]

+close