---
title: "FW 536 — Pre-course exam"
author: "Your Name Here"
date: "`r Sys.Date()`"
output:
  html_document:
    self_contained: true
    toc: true
    toc_depth: 3
    toc_float: true
    code_folding: show
    theme: cosmo
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE, message = FALSE, warning = FALSE)
```

# Instructions

This template matches the [Pre-course exam](pre_course_exam.html). Fill in
each section with your answer. You can use prose, R code, math, or an
embedded photo of hand-written work — whatever is clearest for each
question.

You have 60 minutes. Do not consult outside materials or your classmates.
This exam is graded generously; **guessing is not penalized**, and "I
don't know" is an acceptable answer.

When done: **Knit** to HTML and upload the `.html` to the Canvas
Pre-Course Exam assignment.

---

# Part A — Probability fundamentals (8 points)

## A1. Conditional probability (2 pts)

*Disease prevalence 0.05; test sensitivity 0.92; specificity 0.95.
Given a positive test, what is the probability the animal is infected?*

```{r}
# your work here
```

**Answer:**

## A2. Independence vs mutually exclusive (2 pts)

**Answer:**

## A3. Joint probability (2 pts)

*Two cameras, each detect with probability 0.30. What is P(at least one detects | present)?*

```{r}
# your work here
```

**Answer:**

## A4. Expected value (2 pts)

*Pays \$10,000 if survives, costs \$2,000 if not. P(survival) = 0.7. Expected payoff?*

```{r}
# your work here
```

**Answer:**

---

# Part B — Distributions (8 points)

## B1. Pick the distribution (2 pts)

**a. Number of successful nests out of 12 monitored, with shared independent success probability:**

**b. Number of whale sightings per 1-hour acoustic monitoring period:**

**c. Classification of 100 elk into bulls/cows/calves/yearlings:**

## B2. Mean and variance of Poisson(λ=4) (2 pts)

**Answer:**

## B3. Continuous distribution choice (2 pts)

*Strictly positive, right-skewed response.*

**Answer:**

## B4. Normal probability (2 pts)

*Heights N(152, 8²). Fraction taller than 160 cm?*

```{r}
# you may sketch a Normal curve, mark the threshold, and estimate;
# or use pnorm() to compute exactly.
```

**Answer:**

---

# Part C — Regression (10 points)

## C1. Reading a coefficient (2 pts)

*Slope = 0.8 g/mm. Biological interpretation?*

**Answer:**

## C2. Choosing a GLM (3 pts)

**a. Nest success (yes/no) for 100 nests:**

**b. Birds per 5-minute point count:**

**c. Body mass (g), right-skewed and strictly positive:**

## C3. Log-link interpretation (3 pts)

*Poisson regression coefficient β̂ = 0.30. Effect of a 1-unit increase in x?*

```{r}
# compute exp(0.30) if you remember to
```

**Answer:**

## C4. Logit-link interpretation (2 pts)

*Logistic regression, age coefficient β̂ = -0.5 on logit scale. Effect on odds per year?*

**Answer:**

---

# Part D — Mixed models / hierarchy (8 points)

## D1. When to use a random effect (2 pts)

*12 sites, 6 plots per site. Problem with a single regression that ignores site?*

**Answer:**

## D2. Random vs fixed (3 pts)

**a. Sex (male/female):**

**b. Year (12 years):**

**c. Treatment (control vs exclosure):**

## D3. Shrinkage intuition (3 pts)

**Answer:**

---

# Part E — Likelihood (5 points)

## E1. What is a likelihood? (2 pts)

**Answer:**

## E2. MLE for a proportion (3 pts)

*30 successes in 50 trials. MLE of p?*

```{r}
# your work
```

**Answer:**

---

# Part F — Bayes (8 points)

## F1. Prior, likelihood, posterior (2 pts)

**Prior:**

**Likelihood:**

**Posterior:**

## F2. Posterior interpretation (3 pts)

*95% credible interval (0.2, 0.8). Interpretation and difference from frequentist CI?*

**Answer:**

## F3. Why MCMC (3 pts)

**Answer:**

---

# Part G — Free response (3 points)

## G1. Tell me about your data

*3–5 sentences on the kind of data you work with and a question you'd like to be able to answer after this course.*

**Answer:**

---

# Submission checklist

- [ ] Filled in every section (including "I don't know" where applicable).
- [ ] Knitted to HTML without errors.
- [ ] Embedded any photos with `self_contained: true` (see YAML header).
- [ ] Uploaded the `.html` to Canvas.