You toss a fair tetrahedral (4-sided, and the sides are marked "1", "2", "3", and "4") die, and you play the following game repeatedly. For each game, you throw the die n > 3 times. Starting from the third throw of the current game, right after each throw, you will get 1 dollar if the total number of points on the last three throws is 8 or higher, and you pay 1 dollar otherwise. It is possible to verify that your probability of winning one dollar on the third throw is 0.5. The random variable Xi represents the outcome of the i th throw. Required:
Find the expected value of your total gains/losses over one game in terms of n.

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

substitute,

circle 1 = 5

circle 2 = 20

circle 3 = 44

in this case no matter how you add, you will always get a perfect square..

hence proved

happy to

pls mark as brainliest