# spannd.grid genera las posibles combinaciones
espacio_muestral = expand.grid(c("cara","cruz"),
                               c("cara","cruz"),
                               c("cara","cruz"),
                               c("cara","cruz"),
                               c("cara","cruz"))
names(espacio_muestral)[1] = "lanzamiento_1"
names(espacio_muestral)[2] = "lanzamiento_2"
names(espacio_muestral)[3] = "lanzamiento_3"
names(espacio_muestral)[4] = "lanzamiento_4"
names(espacio_muestral)[5] = "lanzamiento_5"

formato = c("striped", "bordered", "hover", "responsive")

espacio_muestral %>% kable() %>% kable_styling(bootstrap_options = formato,
                                               full_width = FALSE,
                                               position = "center",
                                               font_size = 16) %>% 
  row_spec(0, bold = TRUE, color="darkcyan", align = "center", background = "lightgrey") %>% 
  row_spec(1:nrow(espacio_muestral), bold = TRUE, color="black", align = "center")

class(espacio_muestral)

dim(espacio_muestral)

n_filas = nrow(espacio_muestral)
n_col = ncol(espacio_muestral)
n_filas

n_col

p_total = 1 / 32
p_total

p_0 = p_total * df[1,2]
p_0

p_1 = p_total * df[2,2]
p_1

p_2 = p_total * df[3,2]
p_2

p_3 = p_total * df[4,2]
p_3

p_4 = p_total * df[5,2]
p_4

p_5 = p_total * df[6,2]
p_5

x = c(0,1,2,3,4,5)
n = 5
p = 0.5

f.prob.x = dbinom(x = x, size = n, prob = p)
f.prob.x

df_bin = data.frame(numero_caras = x, Funcion_probabilidad = f.prob.x)

formato = c("striped", "bordered", "hover", "responsive")

df_bin %>% kable() %>% kable_styling(bootstrap_options = formato,
                                               full_width = FALSE,
                                               position = "center",
                                               font_size = 16) %>% 
  row_spec(0, bold = TRUE, color="darkcyan", align = "center", background = "lightgrey") %>% 
  row_spec(1:nrow(df_bin), bold = TRUE, color="black", align = "center")

respuesta4_O_caras <- df_bin$Funcion_probabilidad[df_bin$numero_caras == 0]
respuesta4_O_caras

respuesta4_1_caras <- df_bin$Funcion_probabilidad[df_bin$numero_caras == 1]
respuesta4_1_caras

respuesta4_2_caras <- df_bin$Funcion_probabilidad[df_bin$numero_caras == 2]
respuesta4_2_caras

respuesta4_3_caras <- df_bin$Funcion_probabilidad[df_bin$numero_caras == 3]
respuesta4_3_caras

respuesta4_4_caras <- df_bin$Funcion_probabilidad[df_bin$numero_caras == 4]
respuesta4_4_caras

respuesta4_5_caras <- df_bin$Funcion_probabilidad[df_bin$numero_caras == 5]
respuesta4_5_caras

numero_caras = c(0,1,2,3,4,5)
probabilidad = round(df_bin$Funcion_probabilidad,5)

f_p <- ggplot(data = df_bin, aes(numero_caras, probabilidad)) +
  geom_col(width = 0.7, fill = "darkcyan") +
  labs(title = "Función Probabilidad variable x", x = "Número de veces que sale cara", y = "Probabilidad") +
  theme_gray() + 
  geom_text(label = probabilidad, nudge_y = 0.5, chek_overlap = TRUE)

p = ggplotly(f_p)
p

f_p2 = data.frame(lanzam = 0:5,
                  fun_prob = dbinom (x = 0:5, size = 5, prob = 0.5)) %>% 
  ggplot(aes(x = factor(lanzam), y = fun_prob)) +
  geom_col(width = 0.7, fill = "darkcyan") +
  labs(title = "Función Probabilidad variable x", x = "Número de veces que sale cara", y = "Probabilidad") +
  theme_gray() + 
  geom_text(label = probabilidad, nudge_y = 0.5, chek_overlap = TRUE)
  
p = ggplotly(f_p2)
p

funcion_distribucion = cumsum(probabilidad)
funcion_distribucion

m = matrix(nrow = 6,
           ncol = 1,
           byrow = TRUE,
           dimnames = list(c("0 Caras", "1 Caras", "2 Caras", "3 Caras", "4 Caras", "5 Caras" ),
                           c("Funcion_distribución")))
m_df = as.data.frame(m)

m_df[1,1] = funcion_distribucion[1]
m_df[2,1] = funcion_distribucion[2]
m_df[3,1] = funcion_distribucion[3]
m_df[4,1] = funcion_distribucion[4]
m_df[5,1] = funcion_distribucion[5]
m_df[6,1] = funcion_distribucion[6]


formato = c("striped", "bordered", "hover", "responsive")

m_df %>% kable() %>% kable_styling(bootstrap_options = formato,
                                               full_width = FALSE,
                                               position = "center",
                                               font_size = 16) %>% 
  row_spec(0, bold = TRUE, color="darkcyan", align = "center", background = "lightgrey") %>% 
  row_spec(1:nrow(m_df), bold = TRUE, color="black", align = "center")

x = c(0:5)
n = 5
p = 0.5

f.acum.x = cumsum (dbinom(x = 0:5, size = 5, prob = 0.5))
f.acum.x

x = c(0:5)
n = 5
p = 0.5

f.dis.x = pbinom (x, n,p)
f.dis.x

numero_caras = c(0,1,2,3,4,5)

f_p = ggplot(data = m_df, aes(numero_caras, funcion_distribucion )) +
  geom_line(linetype = 1, color = "darkcyan")+
  labs("Función de distribución variable x  número de caras",
       x = "Número de veces que sale cara",
       y = "Probabilidad acumulada") +
  theme_gray() +
  geom_text(label = funcion_distribucion, nudge_y = 0.05, check_overlap = TRUE)

p = ggplotly(f_p)
p

x = c(0:5)
n = 5
p = 0.5

tabla = data.frame(numero_caras = x,
                   funcion_probabilidad = dbinom(x = x, size = n, prob = p),
                   funcion_distribucion = cumsum(dbinom(x = x, size = n, prob = p)))


formato = c("striped", "bordered", "hover", "responsive")

tabla %>% kable() %>% kable_styling(bootstrap_options = formato,
                                               full_width = FALSE,
                                               position = "center",
                                               font_size = 16) %>% 
  row_spec(0, bold = TRUE, color="darkcyan", align = "center", background = "lightgrey") %>% 
  row_spec(1:nrow(tabla), bold = TRUE, color="black", align = "center")

x_3 = sum(dbinom(0:3, 5, 0.5))
x_3

valor_x = 3
probabilidad = filter(tabla, x == valor_x)
probabilidad

x__3 = pbinom(3, 5, 0.5)
x__3

text_size = 10
margin_size = text_size / 2

f_menor3 = data.frame(lanzam = 0:5,
                      fun_prob = dbinom(0:5, 5, 0.5),
                      fun_dist = pbinom(0:5, 5, 0.5, lower.tail = TRUE))

f_menor3 = f_menor3 %>% 
  mutate(Result = ifelse((lanzam <= 3), "Si", "No"))

f_menor3

p = ggplot(f_menor3, aes(x = lanzam, y = fun_dist, fill = Result)) + 
  geom_col(width = 0.7) + 
  geom_text(aes(label = round(fun_dist, 4), y = fun_dist + 0.2), size = 4, vjust = 0)+
  labs(title = "Probabilidad de que un número de caras sea menor o igual a 3",
       x = "Número de veces obteniendo cara",
       y = "Probabilidad",
       fill = "Resultado") + 
  theme_gray() +
  theme(legend.text = element_text (size = text_size),
        plot.title = element_text (size = text_size,
                                   family = "times",
                                   hjust = 0.5,
                                   vjust = 1,
                                   colour = "darkcyan",
                                   face = "bold",
                                   margin = margin(b = margin_size * 1.2)),
        panel.background = element_rect(fill = "lightgray"),
        panel.grid.major = element_line(color = "white", linewidth = 0.5),
        panel.grid.minor = element_line(color = "white", linewidth = 0.25)) +
  scale_fill_manual(values = c("Si" = "darkcyan", "No" = "black"))

ggplotly(p)

x_2 = sum(dbinom(3:5, 5, 0.5))
x_2

text_size = 10
margin_size = text_size / 2

f_mayor2 = data.frame(lanzam = 0:5,
                      fun_prob = dbinom(0:5, 5, 0.5),
                      fun_dist = pbinom(0:5, 5, 0.5, lower.tail = TRUE))

f_mayor2 = f_mayor2 %>% 
  mutate(Result = ifelse((lanzam > 2), "Si", "No"))

f_mayor2

p = ggplot(f_mayor2, aes(x = lanzam, y = fun_dist, fill = Result)) + 
  geom_col(width = 0.7) + 
  geom_text(aes(label = round(fun_dist, 4), y = fun_dist + 0.2), size = 4, vjust = 0)+
  labs(title = "Probabilidad de que un número de caras sea mayor a 2",
       x = "Número de veces obteniendo cara",
       y = "Probabilidad",
       fill = "Resultado") + 
  theme_gray() +
  theme(legend.text = element_text (size = text_size),
        plot.title = element_text (size = text_size,
                                   family = "times",
                                   hjust = 0.5,
                                   vjust = 1,
                                   colour = "darkcyan",
                                   face = "bold",
                                   margin = margin(b = margin_size * 1.2)),
        panel.background = element_rect(fill = "lightgray"),
        panel.grid.major = element_line(color = "white", linewidth = 0.5),
        panel.grid.minor = element_line(color = "white", linewidth = 0.25)) +
  scale_fill_manual(values = c("Si" = "darkcyan", "No" = "black"))

ggplotly(p)

x_menor_5 = pbinom(5, 5, 0.5)
x_menor_2 = pbinom(2, 5, 0.5)

x_mayor_2 = x_menor_5 - x_menor_2
x_mayor_2

x_1y4 = sum(dbinom(1:4, 5, 0.5))
x_1y4

text_size = 10
margin_size = text_size / 2

f_entre_1y4 = data.frame(lanzam = 0:5,
                      fun_prob = dbinom(0:5, 5, 0.5),
                      fun_dist = pbinom(0:5, 5, 0.5, lower.tail = TRUE))

f_entre_1y4 = f_entre_1y4 %>% 
  mutate(Result = ifelse(lanzam >= 1 & lanzam <= 4, "Si", "No"))

f_entre_1y4

p = ggplot(f_entre_1y4, aes(x = lanzam, y = fun_dist, fill = Result)) + 
  geom_col(width = 0.7) + 
  geom_text(aes(label = round(fun_dist, 4), y = fun_dist + 0.2), size = 4, vjust = 0)+
  labs(title = "Probabilidad de que un número de caras sea mayor a 2",
       x = "Número de veces obteniendo cara",
       y = "Probabilidad",
       fill = "Resultado") + 
  theme_gray() +
  theme(legend.text = element_text (size = text_size),
        plot.title = element_text (size = text_size,
                                   family = "times",
                                   hjust = 0.5,
                                   vjust = 1,
                                   colour = "darkcyan",
                                   face = "bold",
                                   margin = margin(b = margin_size * 1.2)),
        panel.background = element_rect(fill = "lightgray"),
        panel.grid.major = element_line(color = "white", linewidth = 0.5),
        panel.grid.minor = element_line(color = "white", linewidth = 0.25)) +
  scale_fill_manual(values = c("Si" = "darkcyan", "No" = "black"))

ggplotly(p)

x_menor_0 = pbinom(0, 5, 0.5)
x_menor_4 = pbinom(4, 5, 0.5)

x_entre_1y4 = x_menor_4 - x_menor_0
x_entre_1y4

x_2y3 = sum(dbinom(2:3, 5, 0.5))
x_2y3

text_size = 10
margin_size = text_size / 2

f_entre_2y3 = data.frame(lanzam = 0:5,
                      fun_prob = dbinom(0:5, 5, 0.5),
                      fun_dist = pbinom(0:5, 5, 0.5, lower.tail = TRUE))

f_entre_2y3 = f_entre_2y3 %>% 
  mutate(Result = ifelse(lanzam > 1 & lanzam < 4, "Si", "No"))

f_entre_2y3

p = ggplot(f_entre_2y3, aes(x = lanzam, y = fun_dist, fill = Result)) + 
  geom_col(width = 0.7) + 
  geom_text(aes(label = round(fun_dist, 4), y = fun_dist + 0.2), size = 4, vjust = 0)+
  labs(title = "Probabilidad de que un número de caras sea mayor a 2",
       x = "Número de veces obteniendo cara",
       y = "Probabilidad",
       fill = "Resultado") + 
  theme_gray() +
  theme(legend.text = element_text (size = text_size),
        plot.title = element_text (size = text_size,
                                   family = "times",
                                   hjust = 0.5,
                                   vjust = 1,
                                   colour = "darkcyan",
                                   face = "bold",
                                   margin = margin(b = margin_size * 1.2)),
        panel.background = element_rect(fill = "lightgray"),
        panel.grid.major = element_line(color = "white", linewidth = 0.5),
        panel.grid.minor = element_line(color = "white", linewidth = 0.25)) +
  scale_fill_manual(values = c("Si" = "darkcyan", "No" = "black"))

ggplotly(p)

x_menor_1 = pbinom(1, 5, 0.5)
x_menor_3 = pbinom(3, 5, 0.5)

x_entre_2y3 = x_menor_3 - x_menor_1
x_entre_2y3

n = 5
p = 0.5

e_x = n * p

e_x

n = 5
p = 0.5

v_x = n * p * (1 - p)

v_x