Table of contents

1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 53m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample2h 19m
10. Hypothesis Testing for Two Samples3h 22m
11. Correlation1h 6m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

6. Normal Distribution and Continuous Random Variables

Uniform Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Uniform Distribution

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Multiple Choice

Determine if each curve (in orange) is a valid probability density function (i.e. if the total area under the function = 1)

Yes, because the area under the curve = $1$

No, because the area under the curve = $2 is not equal to 1$

No, because probability density functions must be flat

Yes, because the area under the curve = $2 almost equals 1$

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Verified step by step guidance

Step 1: Recall that a probability density function (PDF) must satisfy two conditions: (1) The function must be non-negative for all values of x, and (2) The total area under the curve must equal 1.

Step 2: Analyze the graph provided. The orange curve consists of two segments: a sloped line from x = 2.5 to x = 10, and a flat line from x = 10 to x = 12.5.

Step 3: Calculate the area under the sloped line. The sloped line forms a triangle with a base of (10 - 2.5 = 7.5) and a height of 0.25. Use the formula for the area of a triangle: A = (1/2) * base * height.

Step 4: Calculate the area under the flat line. The flat line forms a rectangle with a base of (12.5 - 10 = 2.5) and a height of 0.2. Use the formula for the area of a rectangle: A = base * height.

Step 5: Add the areas of the triangle and rectangle together to determine the total area under the curve. Compare this total to 1 to verify if the curve is a valid probability density function.