Activity 10

MATH 216: Statistical Thinking

Activity 1: Ecological Research

Scenario: Weekly sightings of blue whales are recorded, with an average of 2.6 sightings.

a. Find the mean and standard deviation.


b. Probability of exactly five sightings:


c. Probability of fewer than two sightings:


Activity 2: Quiz

Question: Given \(\lambda = 4\), what is the probability of observing exactly 2 events?

Options:

    1. \(0.1465\)
    1. \(0.1954\)
    1. \(0.2381\)
    1. \(0.2707\)

Activity 3: Interactive Data Exploration

Task: Use the dpois function to calculate the probability of observing exactly 3 events for different values of \(\lambda\) (e.g., \(\lambda = 1, 2, 3, 4, 5\)). Plot the results using ggplot2.

R Code Example:

Activity 4: Group Activities with Real Data

Task: In a group, analyze a dataset given below of monthly traffic accidents at a busy intersection. The dataset includes the number of accidents per month over a year. Groups should:

  1. Calculate the mean number of accidents per month.

  2. Use the Poisson distribution to calculate the probability of observing exactly 5 accidents in a month.

  3. Create a histogram of the observed data and overlay the Poisson distribution with the calculated \(\lambda\).

Dataset Example: