Maps in Data

Stat 251

2025-04-29

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Graded: homework 11 (functions - really: lists)
Today: last edits for scripts
Thursday: submit your screencast

adding timestamps as chapters

no required attendance in class on Thursday (May 1)

Script

For each of the Things you defined, write out at least three paragraphs:

Make sure to:

include definitions (i.e. how do you measure strength)
give context (i.e. which variables are used)
tie ‘things’ in with the topics in the class

Functions and List

are the extension of vector calculus

(x <- sample(1:10, 15, replace = TRUE))

 [1]  8  8  5  5  6  2  4  5  7  6  1 10 10  4  2

(y <- sample(1:10, 15, replace = TRUE))

 [1]  8  6  8  2 10  9  7  9  7  2  2  4  2  1  1

Add the first element in x to the first element in y:

x[1] + y[1]

[1] 16

Now do that for all elements in x and y:

x + y

 [1] 16 14 13  7 16 11 11 14 14  8  3 14 12  5  3

1:length(x) |> lapply(FUN = function(i) x[i] + y[i]) |> unlist()

 [1] 16 14 13  7 16 11 11 14 14  8  3 14 12  5  3

sum_xy = map(lambda i: r.x[i]+r.y[i], range(1,len(r.x)))
list(sum_xy)

[14, 13, 7, 16, 11, 11, 14, 14, 8, 3, 14, 12, 5, 3]

Your Turn: Graphs of functions

Plot the graph of the function for \(\alpha = \beta = 1/2\) on the interval [0,1]:

\[ f(x) = \frac{1}{B(\alpha, \beta)} x^{\alpha -1} (1 - x)^{\beta - 1} \] \(B(\alpha, \beta)\) is the beta function - a generalization of the (inverse) binomial coefficient. Implemented as beta(a, b) in R, in python use math.gamma and the relationship to the Gamma function \(\Gamma\):

\[ B(a, b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a + b)} \]

Your Turn: Multiple Graphs

Now make \(\alpha\) a vector alpha and plot graphs for values of \(\alpha \in \{ 0.5, 0.6, ..., 1.2\}\)

… can you vectorize \(\beta\) similarly?