library(dplyr)
library(ggplot2)
library(broom)
library(mosaicCalc)

• bind_rows(): stacks 2 or more data.frames on top of each other, matching columns by name.
• mutate(): creates or edits variables in a data.frame.
• summarize(): consolidates many rows of data into a single summary statistic (or several).
• tibble(): creates a data.frame, but fancy! Can reference other vectors within the tibble.

mycoffee

##       style price         shop
## 1     latte     5         <NA>
## 2 cappuccino    4         <NA>
## 3  americano    3         <NA>
## 4     coffee    3 Gimme Coffee
## 5 hot cocoa     2    Starbucks

mycoffee = mycoffee %>%
  mutate(purchased =
    c(5, 4, 10, 2, 1))

mycoffee %>%
  # Summarize data.frame into one row
  summarize(
    # Calculate mean price of drinks
    mean_price = mean(price),
    # Calculate total drinks purchased
    total_purchased = sum(purchased))

##   mean_price total_purchased
## 1        3.4              22

The Ithaca Farmers Market is a vendor-owned cooperative that runs a Saturday-and-Sunday morning market for produce and hand made goods on the Cayuga Lake waterfront. This Saturday, a volunteer tracked 500 customers and recorded how many stalls each customer visited.

• But their spreadsheet got blown away into the lake! Can we still estimate visitation patterns with these statistics?

# Randomly sample 500 visits from a
# poisson distribution with a mean of 5.5
visits = rpois(n = 500, lambda = 5.5)
# Check out the distribution!
visits %>% hist()

# Get the frequency for 5 visits
# in the distribution
pd5 = dpois(5, lambda = 5.5)
# Check it!
pd5

## [1] 0.1714007

# Approximate the PDF of our
# simulated visits
dsim = visits %>% density() %>%
  approxfun()
# Try our density function for
# our simulated data!
dsim(5)

## [1] 0.1759108

# Get the cumulative frequency for a
# value (5) in the distribution
cd5 = ppois(q = 5, lambda = 5.5)
1 - cd5

## [1] 0.4710813

psim = visits %>% density() %>% tidy() %>%
  # Get cumulative probability distribution
  arrange(x) %>%
  # Get cumulative probabilities
  mutate(y = cumsum(y) / sum(y)) %>%
  # Turn it into a literal function!
  approxfun()

# Check it!
psim(5)

## [1] 0.4642488

q5 = qpois(p = c(.25, .75), lambda = 5.5)
# Check it!
q5

## [1] 4 7

qsim = tibble(
  # Get a vector of percentiles from 0 to 1, i
  x = seq(0, 1, by = 0.001),
  # Using our simulated distribution,
  # get the quantiles (values) at those points
  y = visits %>% quantile(probs = x)) %>%
  # Approximate function!
  approxfun()

# Check it!
qsim(c(.25, .75))

## [1] 4 7

P(AB) = P(A) x P(B|A)  →  0.05 = 0.25 x 0.2

2/14 = 5/14 * 2/5

P(A) = ∑_i=1ⁿ P(A|E_i) × P(E_i)

P(C) = P(CS) + P(CS₀)

A local coffee chain needs your help to analyze their supply chain issues. They know that their scones help them sell coffee, but does their coffee help them sell scones?

• Over the last week, when 7 customers bought scones, 3 went on to buy coffee.
• When 3 customers didn't buy scones, just 2 bought coffee.
• In general, 7 out of 10 of customers ever bought scones.
• What's the probability that a customer will buy a scone, given that they just bought coffee?

Can we deduce P(Scone | Coffee) on our own?

• P(S|C) = P(C|S)   x   P(S)   /   P(C)
• 3/5 = 3 / 7   x   7/10   /   5 /10

But what if we don't know P(Coffee)?

• P(C) = P(CS) + P(CS₀)
• P(CS) = P(S) x P(C|S) = P(C) x P(S|C)
• P(CS₀) = P(S₀) x P(C|S₀) = P(C) x P(S₀|C)

• P(C) = P(S) x P(C|S) + P(S₀) x P(C|S₀)
• 5/10 = 7/10 x 3/7   +   3/10 x 2/3