Probability model question

A discrete uniform distribution has the following possible outcome for X[1,2,3,4]. The variance of this distribution is closest to: A. 0.00 B. 1.00 C. 1.25 D. 2.00 My answer MeanX= (1+2+3+4)/4=2.5 Variance = [(1-2.5)^2+(2-2.5)^2+(3-2.5)^2+(4-2.5)^2]/(4-1) But answer key in book used probability weighted model. Actually we can consider X[1,2,3,4] as a sample and can computer variance of sample. I read book but it seem a little bit confusing to me to differentiate when use probability weighted model and when use sample model? By the way, I some time get confuse using formula of Cov, Corr because i still don’t understand clearly their actual meaning. Could anyone pls kindly make clear the meaning of Cov, Corr in actual statistics job? I just want to know what you see or conclude after calculating Cov or Corr. The study note has mention but not clear enough to me. Your comments are appreciated. Thank you!

covariance shows the direction and corelation (used as a measure of diversification)determines the strength of funds in a portfolio.

I got 1.25 using the probability weighted model.

// this is incorrect -> Variance = [(1-2.5)^2+(2-2.5)^2+(3-2.5)^2+(4-2.5)^2]/(4-1) Variance = [(1-2.5)^2+(2-2.5)^2+(3-2.5)^2+(4-2.5)^2]/4 because the population is known -> mean is known. Therefore, variance = 5/4 as Swissaholic pointed out.