Graphing Data 4
- Lecture1.1
  
  Introduction
- Lecture1.2
  
  Basic Charts
- Lecture1.3
  
  Basic Charts Part 2
- Lecture1.4
  
  Randomness
Mean and Standard Deviation 5
- Lecture2.1
  
  Introduction
- Lecture2.2
  
  Random Walk
- Lecture2.3
  
  Random Walk Part 2
- Lecture2.4
  
  Mean and Standard Deviation
- Lecture2.5
  
  Mean and Standard Deviation Part 2
Distributions 6
- Lecture3.1
  
  Introduction
- Lecture3.2
  
  PDF and CDF
- Lecture3.3
  
  PDF and CDF Part 2
- Lecture3.4
  
  Z Scores
- Lecture3.5
  
  Plotting
- Lecture3.6
  
  Solution
Correlation and Linear Regression 7
- Lecture4.1
  
  Introduction
- Lecture4.2
  
  Basics
- Lecture4.3
  
  Correlation
- Lecture4.4
  
  Z-Score
- Lecture4.5
  
  Z-Score Part 2
- Lecture4.6
  
  Linear Regression
- Lecture4.7
  
  Linear Regression Part 2
Probability 3
- Lecture5.1
  
  Introduction
- Lecture5.2
  
  Probability Basics
- Lecture5.3
  
  Probability
Counting Principles 3
- Lecture6.1
  
  Introduction
- Lecture6.2
  
  Factorials and Permutations
- Lecture6.3
  
  Binomial Theorem
Binomial Distribution 3
- Lecture7.1
  
  Introduction
- Lecture7.2
  
  Binomial Distribution
- Lecture7.3
  
  Binomial Distribution Part 2
Confidence Interval 7
- Lecture8.1
  
  Introduction
- Lecture8.2
  
  Alpha
- Lecture8.3
  
  Confidence Intervals
- Lecture8.4
  
  Confidence Intervals Part 2
- Lecture8.5
  
  Confidence Intervals Part 3
- Lecture8.6
  
  Confidence Intervals Part 4
- Lecture8.7
  
  Confidence Intervals Part 5
Proportion Confidence Interval 3
- Lecture9.1
  
  Introduction
- Lecture9.2
  
  Equations
- Lecture9.3
  
  Solution
Hypothesis Testing 5
- Lecture10.1
  
  Introduction
- Lecture10.2
  
  The Null Hypothesis
- Lecture10.3
  
  The Null Hypothesis Part 2
- Lecture10.4
  
  One Tail Test
- Lecture10.5
  
  One Tail Test Part 2
Comparing Two Means 5
- Lecture11.1
  
  Introduction
- Lecture11.2
  
  Known Standard Deviations
- Lecture11.3
  
  Unknown Standard Deviations
- Lecture11.4
  
  Same Unknown Standard Deviations
- Lecture11.5
  
  Solution
Chi-squared Test 3
- Lecture12.1
  
  Introduction
- Lecture12.2
  
  Basics
- Lecture12.3
  
  Expected Values

Z Scores

Solution

print(len(zScores[abs(zScores) < 1])/10000)
print(len(zScores[abs(zScores) < 2])/10000)
print(len(zScores[abs(zScores) < 3])/10000)

It holds up pretty well!

What does the distribution of the z-scores look like?

plt.hist(zScores,bins=100)
plt.show()

Let’s formally define the cdf function.

Equation

$$ CDF(x) = P(X \leq x) $$
$$\text{x = The cutoff point x we want to see if our X is less than or equal to}$$
$$\text{X = Our random variable X}$$

By proxy, if we wanted to see what the probability of our variable being greater than or equal to x was, we could take 1-CDF(x) to get the opposite.

Equation

$$ 1-CDF(x) = P(X \geq x) $$

Now what if we wanted to find the bounds for 1, 2 and 3 standard deviations like we did before, but this time with the CDF function?

Let’s break it down the equation for one standard deviation.

Explanation

Step 1

$$ P(- \sigma < X < \sigma) $$

Step 2

$$ 1-(P(X > \sigma) + P(X < – \sigma))$$

Step 3

$$ 1-(1-CDF(\sigma) + CDF(-\sigma)) $$

Step 4

$$ CDF(\sigma) – CDF(-\sigma) $$

The solution makes sense, we want the probability that we are under a positive standard deviation away, but we do not want to include the probability of being all the way under a negative standard deviation away.

Challenge

Check that we get the correct percentages when we use the cdf function of our distribution.

Prev PDF and CDF Part 2

Next Plotting

Basics

Graphing Data 4

Mean and Standard Deviation 5

Distributions 6

Correlation and Linear Regression 7

Probability 3

Counting Principles 3

Binomial Distribution 3

Confidence Interval 7

Proportion Confidence Interval 3

Hypothesis Testing 5

Comparing Two Means 5

Chi-squared Test 3

Z Scores

Solution

Equation

Equation

Explanation

Step 1

Step 2

Step 3

Step 4

Challenge

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