Understanding Conditional Probability in Uniform Distribution

This video tutorial explains how to determine the conditional probability of a uniform distribution, using the example of an eight-week-old baby's smiling times. It covers two methods: adjusting the probability density function and using the conditional probability formula. The video provides a step-by-step guide to calculating the probability that a baby smiles for more than 12 seconds, given that it smiles for more than 8 seconds, resulting in a probability of approximately 73.33%.

What is the main focus of the video tutorial?

• Understanding conditional probability in uniform distribution

• Exploring the behavior of random variables

• Calculating the average smiling time of a baby

• Learning about different types of probability distributions

What is the range of the uniform distribution for the baby's smiling times?

• 5 to 25 seconds

• 10 to 30 seconds

• 0 to 20 seconds

• 0 to 23 seconds

What is the probability density function value for the original distribution?

• 1/25

• 1/15

• 1/23

• 1/20

What is the new probability density function value when considering the interval from 8 to 23 seconds?

• 1/25

• 1/15

• 1/10

• 1/20

What is the probability that a baby smiles more than 12 seconds given it smiles more than 8 seconds?

• 0.80

• 0.73

• 0.60

• 0.50

What is the base length of the red rectangle used in the probability calculation?

• 15

• 11

• 12

• 10

Which formula is used in the alternative method to find the probability?

• Central Limit Theorem

• Bayes' Theorem

• Conditional Probability Formula

• Total Probability Theorem

What is the probability of x being greater than 12 and greater than 8?

• Probability of x < 12

• Probability of x > 8

• Probability of x > 12

• Probability of x < 8

What is the simplified result of 1/23 divided by itself?

• 1/23

• 1

• 23

• 0

What is the final probability result obtained using both methods?

• 0.80

• 0.73

• 0.60

• 0.50