In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat counterintuitive "null hypothesis" setup we use in intro statistics, because the probability we return (usually in the form of a p-value) is a probability on the sample given constant population parameter set at the null hypothesis values.
I would imagine this is why you see the notation you do in introductory many textbooks.
Answer from Tanner Phillips on Stack ExchangeIm doing some review for my Stats exam coming up. In my notes I wrote down that p^ (p hat) is the expected value while pO is the "observed" or actual value.
So if I were to say the "expected" number of successes is sample size n times p^ or n(p) is that correct? Because on the answer key it said the "expected number of successes" is n(pO) which translates to sample size n times the OBSERVED value.
EDIT: Did some more digging. I looked through the conditions needed to make a inference about a proportion.
One of the conditions was: Ho: pO, n(pO) and n(1-pO) had to be greater than or equal to 10 in order to do a significance test. For the confidenc interval you switch the pO for p.
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Is the sample proportion ($\hat p$) a random variable? - Cross Validated
What is the difference between p and p-hat? Explain. The difference is that p represents the true proportion of a...
How to Calculate PHat?
Difference between pHAT and pO?
How do I find p-hat?
To find p-hat (i.e., sample proportion), you need to follow the next steps:
- Take the number of occurrences of an event or the number of successful outcomes.
- Divide it by the sample size.
- That's all! You have calculated p-hat.
What is the meaning of p-hat?
P-hat coveys the sample proportion, the ratio of certain events or characteristics occurring in a sample to the sample size. It can equal or differ from population proportion, which conveys a proportion of a particular feature associated with a population.
What is a p-value?
In the frequentist tradition (which is what you are using here) the random variable is the data. The population parameters are mathematically treated as constant. This is what leads to the somewhat counterintuitive "null hypothesis" setup we use in intro statistics, because the probability we return (usually in the form of a p-value) is a probability on the sample given constant population parameter set at the null hypothesis values.
I would imagine this is why you see the notation you do in introductory many textbooks.
I don't see a 
in the figure you posted, but from the formula in the figure, 
and 
are statistics. Once you calculate a statistic, it becomes a realization of the random variable (Be aware that I am not saying that your statistic is the true population parameter).
Above all, remember that in most cases upper/lower cases are conventions. They might be widespread, which can be helpful in many cases, but there is no law that forces you to write a random variable's "name" in uppercase. It's common for introductory (and even advanced) books to have a discussion on symbols and style. That section will help you understand the notation the author(s) has adopted.