# use pt() to find probability under the $t$-distribution pt(-3, df = 2) + (1 - pt(3, df = 2))
R calculates starting from the left of the graph. Therefore, to find the area below -3, you just do pt(-3, df=2) whereas you need to subtract the big area to the left of +3 (/starting from the right of the graph until 3) from 1, hence 1-pt(3,df=2)
Under a normal distribution, the area would be about 0.003 using the 68-95-99.7 rule.
Normal rule
With a normal distribution, this would correspond to about 0.05,
How would you find this with a normal distribution mathematically?
# use pt() to find probability under the $t$-distribution pt(-2.10, df = 18) #> [1] 0.025
worked example in R
In R, the function used for calculating probabilities under a ttt-distribution is pt() (which should seem similar to previous R functions, pnorm() and pchisq()). Don’t forget that with the ttt-distribution, the degrees of freedom must always be specified!
How to do this statistical stuff in R!!!
However, its tails are thicker than the normal distribution’s, meaning observations are more likely to fall beyond two standard deviations from the mean than under the normal distribution.
This is what Dr. Herring meant by "fatter tails."
Below is why.
What responsibility does a writer bear when construing Utopian or dystopian alternatives to our contemporary world? Are writersof fairy tales unethical and irresponsible when they create false happyendings and delude us into believing that harmony is possible in ourrapidly changing postmodern globalized war-torn world? Is it unethicalto publish fairy tales in all their mass-mediated modes to make as muchprofit as one can by playing with our Utopian desires?
I never thought about this responsibility! But i think the rest is hyperbolic.. the responsibility does not solely fall on the writer, but also the reader's representation