Preparing your learning workspace

STATLAB Academy | Learn Statistics with R and Real-World Data

Interactive Mission

discrete model selector

Discrete model selector

Choose a model from process structure, not surface keywords.

Selected value x

Process structureFinite sampling without replacementTrials until first successEvents in a fixed exposure

P(X = x)

0.2

F(x) = P(X <= x)

0.9

E(X)

SD(X)

1.0954

Probability mass across the support

Accessible probability table
x	P(X=x)	Included in F(4)
1	0.1	Yes
2	0.2	Yes
3	0.4	Yes
4	0.2	Yes
5	0.1	No

Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.

Interactive Mission

discrete distribution capstone

Service-risk decision builder

Compare staffing, audit, and outreach assumptions before writing a recommendation.

Selected value x

Process structureFinite sampling without replacementTrials until first successEvents in a fixed exposure

P(X = x)

0.2

F(x) = P(X <= x)

0.9

E(X)

SD(X)

1.0954

Probability mass across the support

Accessible probability table
x	P(X=x)	Included in F(4)
1	0.1	Yes
2	0.2	Yes
3	0.4	Yes
4	0.2	Yes
5	0.1	No

Interpretation: Custom PMF, discrete uniform, Bernoulli, or binomial: inspect support and trial structure before choosing.

R connection

R note: Service Operations Risk Capstone

Run and edit the original script, inspect intermediate output, and keep exact and approximate results clearly labelled.

Live R Lab

Service Operations Risk Capstone

Integrate discrete models into an auditable operating-plan comparison.

Dataset CSV

Editable R code

# Module 6 R Note 14: Service operations risk capstone
operations <- read.csv("module6_service_risk_capstone.csv")
print(head(operations))
print(str(operations))
print(colSums(is.na(operations)))

arrival_pmf <- prop.table(table(operations$customer_arrivals))
arrival_x <- as.numeric(names(arrival_pmf))
print(data.frame(x = arrival_x, pmf = as.numeric(arrival_pmf),
                 cdf = cumsum(as.numeric(arrival_pmf))))
print(data.frame(expected_arrivals = weighted.mean(arrival_x, arrival_pmf),
                 arrival_sd = sqrt(weighted.mean((arrival_x - weighted.mean(arrival_x, arrival_pmf))^2, arrival_pmf))))

n_services <- 30
p_late <- sum(operations$late_services) / sum(operations$services_completed)
lambda <- mean(operations$customer_arrivals)
print(c(binomial_at_least_6_late = pbinom(5, n_services, p_late, lower.tail = FALSE),
        poisson_more_than_18_arrivals = ppois(18, lambda, lower.tail = FALSE)))

lot <- head(operations, 1)
print(dhyper(2, m = lot$defective_items, n = lot$items_in_lot - lot$defective_items,
             k = lot$audit_sample_size))
conversion_p <- mean(1 / operations$first_conversion_contact)
print(c(geometric_within_5 = pgeom(5 - 1, conversion_p),
        expected_contacts = 1 / conversion_p))

cost <- operations$fixed_staffing_cost +
  operations$variable_service_cost * operations$services_completed +
  operations$shortage_penalty * pmax(operations$customer_arrivals - operations$services_completed, 0)
aggregate_demand <- operations$region_a_demand + operations$region_b_demand
print(data.frame(mean_cost = mean(cost), sd_cost = sd(cost),
                 mean_regional_demand = mean(aggregate_demand),
                 covariance = cov(operations$region_a_demand, operations$region_b_demand)))
par_old <- par(mfrow = c(1, 3))
hist(operations$customer_arrivals, main = "Arrivals", xlab = "Customers")
barplot(arrival_pmf, main = "Empirical arrival PMF", ylab = "Probability")
plot(operations$region_a_demand, operations$region_b_demand,
     main = "Regional demand", xlab = "Region A", ylab = "Region B")
par(par_old)
print("Decision scaffold: compare plans, disclose assumptions and approximations, then write your own recommendation.")

Results

Ready to run

Ready to run. Results, errors, tables, plots, and fallback messages will appear here.

Define and validate the model.

Print auditable calculations.

Interpret assumptions and limitations.

Preparing your learning workspace

Module 6 Capstone: Service Operations Risk Model

Discrete-model reasoning

Concept map

Model selection

Plan comparison

Disclosure

Decision synthesis

discrete model selector

Discrete model selector

discrete distribution capstone

Service-risk decision builder

Service operations risk

R note: Service Operations Risk Capstone

Service Operations Risk Capstone

Results

Pause and write

Ask your distribution coach

Lesson checkpoint

Module 6 Lesson 18 Checkpoint

A capstone reports Poisson values in place of exact binomial values. What must it disclose?

Recommended reading

Module 6 learning material