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How would I express the following concept in accepted mathematical notation? :

As variable a plus variable b approach infinity the probability of event c occurring approaches 1.

and,

the probability of b is directly proportional to a

I want to acknowledge that I may be coming across as a crazy person in my ignorance

Thanks in advance!

Yama Raja
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  • Hi, welcome to Math SE. I notice $b$ is a number in the first example, but an event in the second. Are they meant to mean different things? That would be understandable if you wanted to use the earliest letters of the alphabet you can in each, but please make sure to give each symbol only one meaning throughout a document discussing multiple examples. – J.G. Oct 07 '23 at 07:50
  • Thank you so much for the warm welcome! I confess I'm a bit nervous. But let's get to it. I was just worrying about what you helped clarify with your question since var a and var b are independent (I think). OK, just started realizing after doing some honest research that I'm out over my skis, Here: var a is the size of a tumor though not necessarily in a ?integer fashion , i.e could be four categories of size with category 1 being < 1 cm in size. variable b would be a ?nonparametric value placed on a clinicians skill. The Prob of C is a correct diagnosis is made. – Yama Raja Oct 07 '23 at 08:05
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    Statisticians often capitalize random variables while leaving their values lower-case. Maybe you wanted $\lim_{a+b\to\infty}\mathbb{P}(c)=1,,\mathbb{P}(B=b)\propto a$ (I'm not sure why @AaaLol_dude's answer uses $\mathbb{P}(a)$ in the second example). – J.G. Oct 07 '23 at 08:16
  • Yes, I think I'm following you somewhat on the.. (apologies. I haven't learned your formatting yet and I'm being impatient) second ?term where you wrote the Probability of event B is directly proportional to the value of a. Because what I'm really trying to describe with my clumsy notation with "b" is the probability the clinician with a constant skill is able to find the tumor on a given point in time. I think. I'm going to pack it in for the night. And seriously, thank you. I would love a rec for a beginner level student of middle age for a course/book on probability and statistics – Yama Raja Oct 07 '23 at 08:32

1 Answers1

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First one: $$\lim_{{a+b} \to \infty}\mathbb{P}(c) = 1$$ where $\mathbb{P}$ is the probability function.

Second one:

$$\exists k \ni \forall b, \mathbb{P}(b) = k \times \mathbb{P}(a)$$

Aaa Lol_dude
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