Espacios muestrales de eventos de variables binomiales y multinomales

Paquetes y fuentes

prob, ggraph,igraph,tidyverse

https://cran.r-project.org/web/packages/prob/vignettes/prob.pdf

https://stackoverflow.com/questions/25692325/list-the-sample-space

https://www.r-graph-gallery.com/334-basic-dendrogram-with-ggraph.html

https://www.r-graph-gallery.com/335-custom-ggraph-dendrogram.html

Variable dicotómica, dos resultados posibles como cara o cruz (H,T) y 8 eventos

# create an edge list data frame giving the binomial dos opciones ocho enventos
d1 <- data.frame(from="origen", to=paste("rama", seq(1,2), sep=""))
d2 <- data.frame(from=rep(d1$to, each=2), to=paste("srama", seq(1,4), sep="_"))
d3 <- data.frame(from=rep(d2$to, each=2), to=paste("ssrama", seq(1,8), sep="_"))
d4 <- data.frame(from=rep(d3$to, each=2), to=paste("sssrama", seq(1,16), sep="_"))
d5 <- data.frame(from=rep(d4$to, each=2), to=paste("ssssrama", seq(1,32), sep="_"))
d6 <- data.frame(from=rep(d5$to, each=2), to=paste("sssssrama", seq(1,64), sep="_"))
d7 <- data.frame(from=rep(d6$to, each=2), to=paste("ssssssrama", seq(1,128), sep="_"))
d8 <- data.frame(from=rep(d7$to, each=2), to=paste("sssssssrama", seq(1,256), sep="_"))

edges <- rbind(d1, d2, d3,d4,d5,d6,d7,d8)
edges$res<-ifelse(as.integer(substrRight(as.character(edges$to),1))%% 2 == 0, "T","H")

mygraph <- graph_from_data_frame(edges)
ggraph(mygraph, layout = 'dendrogram', circular = FALSE) + 
  geom_edge_diagonal(aes(color = as.factor(res))) +
  geom_node_point() +
  theme_void()

espm<-tosscoin(8)
espm %>% 
  kable() %>%
  kable_styling(full_width = F,font_size = 8)
toss1 toss2 toss3 toss4 toss5 toss6 toss7 toss8
H H H H H H H H
T H H H H H H H
H T H H H H H H
T T H H H H H H
H H T H H H H H
T H T H H H H H
H T T H H H H H
T T T H H H H H
H H H T H H H H
T H H T H H H H
H T H T H H H H
T T H T H H H H
H H T T H H H H
T H T T H H H H
H T T T H H H H
T T T T H H H H
H H H H T H H H
T H H H T H H H
H T H H T H H H
T T H H T H H H
H H T H T H H H
T H T H T H H H
H T T H T H H H
T T T H T H H H
H H H T T H H H
T H H T T H H H
H T H T T H H H
T T H T T H H H
H H T T T H H H
T H T T T H H H
H T T T T H H H
T T T T T H H H
H H H H H T H H
T H H H H T H H
H T H H H T H H
T T H H H T H H
H H T H H T H H
T H T H H T H H
H T T H H T H H
T T T H H T H H
H H H T H T H H
T H H T H T H H
H T H T H T H H
T T H T H T H H
H H T T H T H H
T H T T H T H H
H T T T H T H H
T T T T H T H H
H H H H T T H H
T H H H T T H H
H T H H T T H H
T T H H T T H H
H H T H T T H H
T H T H T T H H
H T T H T T H H
T T T H T T H H
H H H T T T H H
T H H T T T H H
H T H T T T H H
T T H T T T H H
H H T T T T H H
T H T T T T H H
H T T T T T H H
T T T T T T H H
H H H H H H T H
T H H H H H T H
H T H H H H T H
T T H H H H T H
H H T H H H T H
T H T H H H T H
H T T H H H T H
T T T H H H T H
H H H T H H T H
T H H T H H T H
H T H T H H T H
T T H T H H T H
H H T T H H T H
T H T T H H T H
H T T T H H T H
T T T T H H T H
H H H H T H T H
T H H H T H T H
H T H H T H T H
T T H H T H T H
H H T H T H T H
T H T H T H T H
H T T H T H T H
T T T H T H T H
H H H T T H T H
T H H T T H T H
H T H T T H T H
T T H T T H T H
H H T T T H T H
T H T T T H T H
H T T T T H T H
T T T T T H T H
H H H H H T T H
T H H H H T T H
H T H H H T T H
T T H H H T T H
H H T H H T T H
T H T H H T T H
H T T H H T T H
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H H H T H T T H
T H H T H T T H
H T H T H T T H
T T H T H T T H
H H T T H T T H
T H T T H T T H
H T T T H T T H
T T T T H T T H
H H H H T T T H
T H H H T T T H
H T H H T T T H
T T H H T T T H
H H T H T T T H
T H T H T T T H
H T T H T T T H
T T T H T T T H
H H H T T T T H
T H H T T T T H
H T H T T T T H
T T H T T T T H
H H T T T T T H
T H T T T T T H
H T T T T T T H
T T T T T T T H
H H H H H H H T
T H H H H H H T
H T H H H H H T
T T H H H H H T
H H T H H H H T
T H T H H H H T
H T T H H H H T
T T T H H H H T
H H H T H H H T
T H H T H H H T
H T H T H H H T
T T H T H H H T
H H T T H H H T
T H T T H H H T
H T T T H H H T
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H H H H T H H T
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H H T T T H H T
T H T T T H H T
H T T T T H H T
T T T T T H H T
H H H H H T H T
T H H H H T H T
H T H H H T H T
T T H H H T H T
H H T H H T H T
T H T H H T H T
H T T H H T H T
T T T H H T H T
H H H T H T H T
T H H T H T H T
H T H T H T H T
T T H T H T H T
H H T T H T H T
T H T T H T H T
H T T T H T H T
T T T T H T H T
H H H H T T H T
T H H H T T H T
H T H H T T H T
T T H H T T H T
H H T H T T H T
T H T H T T H T
H T T H T T H T
T T T H T T H T
H H H T T T H T
T H H T T T H T
H T H T T T H T
T T H T T T H T
H H T T T T H T
T H T T T T H T
H T T T T T H T
T T T T T T H T
H H H H H H T T
T H H H H H T T
H T H H H H T T
T T H H H H T T
H H T H H H T T
T H T H H H T T
H T T H H H T T
T T T H H H T T
H H H T H H T T
T H H T H H T T
H T H T H H T T
T T H T H H T T
H H T T H H T T
T H T T H H T T
H T T T H H T T
T T T T H H T T
H H H H T H T T
T H H H T H T T
H T H H T H T T
T T H H T H T T
H H T H T H T T
T H T H T H T T
H T T H T H T T
T T T H T H T T
H H H T T H T T
T H H T T H T T
H T H T T H T T
T T H T T H T T
H H T T T H T T
T H T T T H T T
H T T T T H T T
T T T T T H T T
H H H H H T T T
T H H H H T T T
H T H H H T T T
T T H H H T T T
H H T H H T T T
T H T H H T T T
H T T H H T T T
T T T H H T T T
H H H T H T T T
T H H T H T T T
H T H T H T T T
T T H T H T T T
H H T T H T T T
T H T T H T T T
H T T T H T T T
T T T T H T T T
H H H H T T T T
T H H H T T T T
H T H H T T T T
T T H H T T T T
H H T H T T T T
T H T H T T T T
H T T H T T T T
T T T H T T T T
H H H T T T T T
T H H T T T T T
H T H T T T T T
T T H T T T T T
H H T T T T T T
T H T T T T T T
H T T T T T T T
T T T T T T T T 
ggraph(mygraph, layout = 'kk', circular = FALSE) + 
  geom_edge_diagonal(aes(color = as.factor(res))) +
  geom_node_point() +
  theme_void()

Espacios muestrales de variable con tres resultados posibles como sería ganar, perder o empatar en cinco eventos

# create an edge list data frame giving the multinomial tres opciones cinco enventos
d1 <- data.frame(from="origien", to=paste("rama", seq(1,3), sep=""))
d2 <- data.frame(from=rep(d1$to, each=3), to=paste("srama", seq(1,9), sep="_"))
d3 <- data.frame(from=rep(d2$to, each=3), to=paste("ssrama", seq(1,27), sep="_"))
d4 <- data.frame(from=rep(d3$to, each=3), to=paste("sssrama", seq(1,81), sep="_"))
d5 <- data.frame(from=rep(d4$to, each=3), to=paste("ssssrama", seq(1,243), sep="_"))

edges <- rbind(d1, d2, d3,d4,d5)
edges$res<-ifelse(as.integer(substrRight(as.character(edges$to),1)) %in% c(1,4,7),"P", 
           ifelse(as.integer(substrRight(as.character(edges$to),1)) %in% c(2,5,8),"E","G"))

mygraph <- graph_from_data_frame(edges)
ggraph(mygraph, layout = 'dendrogram', circular = FALSE) + 
  geom_edge_diagonal(aes(color = as.factor(res))) +
  geom_node_point() +
  theme_void()

espm<-urnsamples(1:3, size = 5, replace = TRUE, ordered = TRUE)
espm %>% 
  kable() %>%
  kable_styling(full_width = F,font_size = 8)
X1 X2 X3 X4 X5
1 1 1 1 1
2 1 1 1 1
3 1 1 1 1
1 2 1 1 1
2 2 1 1 1
3 2 1 1 1
1 3 1 1 1
2 3 1 1 1
3 3 1 1 1
1 1 2 1 1
2 1 2 1 1
3 1 2 1 1
1 2 2 1 1
2 2 2 1 1
3 2 2 1 1
1 3 2 1 1
2 3 2 1 1
3 3 2 1 1
1 1 3 1 1
2 1 3 1 1
3 1 3 1 1
1 2 3 1 1
2 2 3 1 1
3 2 3 1 1
1 3 3 1 1
2 3 3 1 1
3 3 3 1 1
1 1 1 2 1
2 1 1 2 1
3 1 1 2 1
1 2 1 2 1
2 2 1 2 1
3 2 1 2 1
1 3 1 2 1
2 3 1 2 1
3 3 1 2 1
1 1 2 2 1
2 1 2 2 1
3 1 2 2 1
1 2 2 2 1
2 2 2 2 1
3 2 2 2 1
1 3 2 2 1
2 3 2 2 1
3 3 2 2 1
1 1 3 2 1
2 1 3 2 1
3 1 3 2 1
1 2 3 2 1
2 2 3 2 1
3 2 3 2 1
1 3 3 2 1
2 3 3 2 1
3 3 3 2 1
1 1 1 3 1
2 1 1 3 1
3 1 1 3 1
1 2 1 3 1
2 2 1 3 1
3 2 1 3 1
1 3 1 3 1
2 3 1 3 1
3 3 1 3 1
1 1 2 3 1
2 1 2 3 1
3 1 2 3 1
1 2 2 3 1
2 2 2 3 1
3 2 2 3 1
1 3 2 3 1
2 3 2 3 1
3 3 2 3 1
1 1 3 3 1
2 1 3 3 1
3 1 3 3 1
1 2 3 3 1
2 2 3 3 1
3 2 3 3 1
1 3 3 3 1
2 3 3 3 1
3 3 3 3 1
1 1 1 1 2
2 1 1 1 2
3 1 1 1 2
1 2 1 1 2
2 2 1 1 2
3 2 1 1 2
1 3 1 1 2
2 3 1 1 2
3 3 1 1 2
1 1 2 1 2
2 1 2 1 2
3 1 2 1 2
1 2 2 1 2
2 2 2 1 2
3 2 2 1 2
1 3 2 1 2
2 3 2 1 2
3 3 2 1 2
1 1 3 1 2
2 1 3 1 2
3 1 3 1 2
1 2 3 1 2
2 2 3 1 2
3 2 3 1 2
1 3 3 1 2
2 3 3 1 2
3 3 3 1 2
1 1 1 2 2
2 1 1 2 2
3 1 1 2 2
1 2 1 2 2
2 2 1 2 2
3 2 1 2 2
1 3 1 2 2
2 3 1 2 2
3 3 1 2 2
1 1 2 2 2
2 1 2 2 2
3 1 2 2 2
1 2 2 2 2
2 2 2 2 2
3 2 2 2 2
1 3 2 2 2
2 3 2 2 2
3 3 2 2 2
1 1 3 2 2
2 1 3 2 2
3 1 3 2 2
1 2 3 2 2
2 2 3 2 2
3 2 3 2 2
1 3 3 2 2
2 3 3 2 2
3 3 3 2 2
1 1 1 3 2
2 1 1 3 2
3 1 1 3 2
1 2 1 3 2
2 2 1 3 2
3 2 1 3 2
1 3 1 3 2
2 3 1 3 2
3 3 1 3 2
1 1 2 3 2
2 1 2 3 2
3 1 2 3 2
1 2 2 3 2
2 2 2 3 2
3 2 2 3 2
1 3 2 3 2
2 3 2 3 2
3 3 2 3 2
1 1 3 3 2
2 1 3 3 2
3 1 3 3 2
1 2 3 3 2
2 2 3 3 2
3 2 3 3 2
1 3 3 3 2
2 3 3 3 2
3 3 3 3 2
1 1 1 1 3
2 1 1 1 3
3 1 1 1 3
1 2 1 1 3
2 2 1 1 3
3 2 1 1 3
1 3 1 1 3
2 3 1 1 3
3 3 1 1 3
1 1 2 1 3
2 1 2 1 3
3 1 2 1 3
1 2 2 1 3
2 2 2 1 3
3 2 2 1 3
1 3 2 1 3
2 3 2 1 3
3 3 2 1 3
1 1 3 1 3
2 1 3 1 3
3 1 3 1 3
1 2 3 1 3
2 2 3 1 3
3 2 3 1 3
1 3 3 1 3
2 3 3 1 3
3 3 3 1 3
1 1 1 2 3
2 1 1 2 3
3 1 1 2 3
1 2 1 2 3
2 2 1 2 3
3 2 1 2 3
1 3 1 2 3
2 3 1 2 3
3 3 1 2 3
1 1 2 2 3
2 1 2 2 3
3 1 2 2 3
1 2 2 2 3
2 2 2 2 3
3 2 2 2 3
1 3 2 2 3
2 3 2 2 3
3 3 2 2 3
1 1 3 2 3
2 1 3 2 3
3 1 3 2 3
1 2 3 2 3
2 2 3 2 3
3 2 3 2 3
1 3 3 2 3
2 3 3 2 3
3 3 3 2 3
1 1 1 3 3
2 1 1 3 3
3 1 1 3 3
1 2 1 3 3
2 2 1 3 3
3 2 1 3 3
1 3 1 3 3
2 3 1 3 3
3 3 1 3 3
1 1 2 3 3
2 1 2 3 3
3 1 2 3 3
1 2 2 3 3
2 2 2 3 3
3 2 2 3 3
1 3 2 3 3
2 3 2 3 3
3 3 2 3 3
1 1 3 3 3
2 1 3 3 3
3 1 3 3 3
1 2 3 3 3
2 2 3 3 3
3 2 3 3 3
1 3 3 3 3
2 3 3 3 3
3 3 3 3 3 
ggraph(mygraph, layout = 'gem', circular = FALSE) + 
  geom_edge_diagonal(aes(color = as.factor(res))) +
  geom_node_point() +
  theme_void()

Espacios muestrales de variable de cuatro resultados como una ruleta de cuatro colores en 4 eventos

# create an edge list data frame giving multinomilas cuatro opciones cuatro enventos
d1 <- data.frame(from="origien", to=paste("rama", seq(1,4), sep=""))
d2 <- data.frame(from=rep(d1$to, each=4), to=paste("srama", seq(1,16), sep="_"))
d3 <- data.frame(from=rep(d2$to, each=4), to=paste("ssrama", seq(1,64), sep="_"))
d4 <- data.frame(from=rep(d3$to, each=4), to=paste("sssrama", seq(1,256), sep="_"))


edges <- rbind(d1, d2, d3,d4)
edges$res<-ifelse(((as.integer(substrRight(as.character(edges$to),1))/4)%%1) == 0,"R",
                  ifelse(((as.integer(substrRight(as.character(edges$to),1))/4)%%1) == .75,"V",
                         ifelse(((as.integer(substrRight(as.character(edges$to),1))/4)%%1) == .5,"A","N")))


mygraph <- graph_from_data_frame(edges)
ggraph(mygraph, layout = 'dendrogram', circular = FALSE) + 
  geom_edge_diagonal(aes(color = as.factor(res))) +
  geom_node_point() +
  theme_void()

espm<-urnsamples(1:4, size = 2, replace = TRUE, ordered = TRUE)
espm %>% 
  kable() %>%
  kable_styling(full_width = F,font_size = 8)
X1 X2
1 1
2 1
3 1
4 1
1 2
2 2
3 2
4 2
1 3
2 3
3 3
4 3
1 4
2 4
3 4
4 4 
ggraph(mygraph, layout = 'circle', circular = FALSE) + 
  geom_edge_diagonal(aes(color = as.factor(res))) +
  geom_node_point() +
  theme_void()