Final answer:
The provided statement is not clearly a true or false question due to apparent typos or incompleteness. However, survival functions are statistical tools used to describe the probability of survival beyond a certain time point, and the calculations vary based on distribution types like Type I or Type II curves.
Step-by-step explanation:
The question seems to be focused on the concept of survival functions and probabilities, which are fundamental topics in statistics, a branch of mathematics. However, the statement provided by the student, 'true or false- for any given survival function, we have e20=1 e21', appears incomplete or contains typos and thus cannot be directly addressed as a true or false question. Nevertheless, we can clarify some key concepts related to survival functions and probabilities to provide assistance.
Survival functions are used to describe the probability of an individual or an item surviving past a certain point in time. The probability notated as P(x > 20) signifies the probability of survival beyond a particular time, in this case, after 20 units (which could be minutes, days, years, etc.). It is incorrect to compare probabilities like e20 to a constant value such as 1 e21 without further context, as probabilities are calculated using statistical distributions.
It's also relevant to understand that probabilities for individuals may differ from probabilities calculated for means when different distributions are involved. For example, Type I survivorship curves describe situations where the likelihood of survival decreases consistently (like losing 20% of a population each year), while Type II survivorship curves describe a constant mortality rate over time.