Chapter 3 suggestions
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arianagamero commented
3.3 Expected value
In order to calculate the mean using R, you will need to generate 2 different sets of variables for the values (x) and their respective probabilities (px).
x <- 1:5
px <- c(.1, .15, .2, .25, .3)
Then, you multiply these two datasets and find the sum of the weighted probabilities:
x*px
sum(x*px) # E(X)
You can also do this in the following way:
weighted.mean(x, px)
3.3 Variance
You can calculate the variance in 2 ways:
- Manually computing the variance formula where you find the sum of the squared differences of each value with the mean
x - 3.5
(x - 3.5)^2
((x - 3.5)^2)*px
sum(((x - 3.5)^2)*px) # V(X)
- Using the fact that E(X^2) - [E(X)]^2 (find these two values using the formula for expectation):
x
px
x^2
(x^2)*px
sum((x^2)*px) # E(X^2)
14-3.5^2 # E(X^2) - [E(X)]^2
I think the sections on Binomial, Poisson and Hypergeometric distributions are very well explained and complete