Understanding Probability Density Functions

Understanding Probability Density Functions

Assessment

Interactive Video

Mathematics, Science

9th - 12th Grade

Practice Problem

Hard

Created by

Amelia Wright

FREE Resource

The video explores probability density functions (PDFs) using a continuous random variable G. It explains how to construct a legitimate PDF by calculating the necessary height for the function. The video also covers how to calculate probabilities for specific ranges of G, including the probability of G being exactly a value, which is zero. Finally, it delves into philosophical considerations of probability calculations, emphasizing the concept of zero probability for exact values.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is a probability density function (PDF) used for?

To determine the probability of discrete outcomes

To find the median of a dataset

To describe the likelihood of a continuous random variable

To calculate the mean of a dataset

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How does the PDF behave outside the range of 1 to 5?

It is zero

It decreases exponentially

It is constant

It increases linearly

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What must the total area under a probability density function equal?

0

1

The range of the variable

The height of the curve

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How is the height of a PDF determined for a uniform distribution between 1 and 5?

By using the standard deviation

By calculating the mean of the range

By ensuring the area under the curve equals 1

By dividing the range by the total area

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the base length of the PDF between 1 and 5?

6

3

4

5

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the probability that G is between 2 and 3, including both values?

1

1/4

1/2

3/8

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What shape is used to calculate the area under the curve between 2 and 3?

Trapezoid

Circle

Triangle

Rectangle

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