7. Exercises and Tutorials

Chapter 2: The Frequency Distribution

• Exercise c01-01 - Constructing a Frequency Distribution Graph
  
  
• Tutorial - How to import a text file into Excel
  
  
• Tutorial - How to construct a Frequency Distribution in Excel
  
  
• Question 1: What do you learn about your data from a frequency distribution?
  
  
  

Chapter 2: The Relative Frequency Distribution

• Exercise c02-01 - Constructing a Relative Frequency Distribution
  
  
• Exercise c02-02 - Implement frequency distribution on Satellite Images
  
  
• Question 1: The Relative Frequency Distribution or histogram for the whole image has three peaks, whilst those for sand and water do not. Why is this?
  
  
• Question 2: The histogram for plantation does not either. Why not?
  
  
• Question 3: What cover types are represented in the three peaks in the histogram for the whole image?
  
  

Chapter 2: Measures of Value

• Exercise c03-01 - Using ILWIS for histogram calculation
  
  
• Question 1: In the histogram, the mean, median and mode are all marked as lines, with symbols (A), (B) and (C) against the lines. Which line represents the mean, the mode and the median?
  
  
• Question 2: We have discussed here the sample mean, $$\overline{x}$$. What is the population mean, µ and does the population mean vary from the sample mean and if so, why?
  
  
• Questions 3: If we call the differences between the individual observations, $x_1,x_2,\dots ,x_n$ and the mean, $\overline{x}$, the residuals, then show, using a set of data, that the smallest sums of squares of the residuals occurs when using the mean value, that is
  $Sof{S}_{smallest}={\sum \{x_1-\overline{x}\}}^2$
  
  

Chapter 2: The Multi-Dimensional Frequency Distribution

• Exercise c05-ws01 - Constructing scattergrams
  
  

Chapter 2: Covariance and Correlation

• Exercise c06-ws01 - Correlation in Satellite Data
  
  

Chapter 2: Probability

• Question 1: What is the probability of at least one six?
  
  
• Question 2: What is the probability of getting 6 as the sum of the two dice?
  
  
• Question 3: If Pie in the Sky wins the first race, what is the probability that Doughboy will win the second?
  
  
• Question 4: What is the Probability that Raddish will win both races?
  
  
• Question 5: What is the most likely combination to win?
  
  
• Question 6: You want to make more than one bet on winning both races so that you have a probability of 25% or more that one of your combinations wins. What is the fewest number of combinations that you must select to reach 30%?
  
  
• Question 7: In a deck of 52 cards, containing four suits, what is the probability of getting a King in the next dealt card?
  
  
• Question 8: You are dealt a hand of 5 cards from a 52 card pack. What is the probability of getting an Ace?
  
  
• Question 9: Again you are dealt five cards. What is the probability of getting five spades?
  
  

Chapter 2: Binomial Distribution

• Question 1: What is the theoretical PDF for selecting a card at random of a particular number or rank (such as an Ace, 2, 3, ?, Jack, etc) from a pack of 52 cards? (Shuffle a pack of 52 cards and then select a single card. Repeat this process 30 times so as to derive a sample PDF to address the question)
  
  
• Question 2: If you shuffle the pack once and then select 30 cards at random from the pack, how does this PDF vary from the PDF derived in Question 1?
  
  

Chapter 2: Normal Distribution

• Question 1: What is the probability that a value will occur within one standard deviation of the mean that is Pr{(-1≤z≤1)|N(0,1)}?
  
  
• Question 2: What is the probability that a value will occur in the range 8 to 12 in the Normal PDF, N(10,4)? Convert the x=8 and 12 to z values first.
  
  
• Question 3: What is the value of the probability,
  Pr{(10≤x≤14)|N(10,4)}?
  
  
• Question 4: What is the value of the probability,
  Pr{(9≤x≤14)|N(10,4)}?
  
  
• Question 5: What is the value of the probability,
  Pr{(11≤x≤15)|N(10,4)}?
  
  
  
• Question 6: What is the value of the probability,
  Pr{(x>12)|N(10,4)}?