Which of these is NOT an application of the Law of Large Numbers in data science?
Building a spam filter by analyzing the characteristics of millions of emails.
Predicting the outcome of a single coin toss based on past tosses.
Developing an insurance pricing model based on historical claims data.
Estimating the click-through rate of an online advertisement.
The time until a radioactive particle decays is modeled by an exponential distribution. If the average decay time is 10 seconds, what is the median decay time?
6.93 seconds
10 seconds
14.43 seconds
5 seconds
Events A and B are independent. The probability of A occurring is 0.4, and the probability of B occurring is 0.6. What is the probability that at least one of the events, A or B, will occur?
1.00
0.24
0.50
0.76
Suppose 30% of people in a city own a car and 20% own a bicycle. If car ownership and bicycle ownership are independent, what is the probability that a randomly selected person owns both a car and a bicycle?
6%
Cannot be determined
50%
10%
In a normal distribution, what percentage of data falls within three standard deviations of the mean?
99.73%
100%
95.45%
68.27%
What does a conditional probability P(Y=y | X=x) represent in the context of joint distributions?
The probability of X = x, given no information about Y
The probability of Y = y, given that X is known to have the value x
The probability of Y = y, given no information about X
The probability of X = x and Y = y occurring simultaneously
A company wants to analyze its website traffic. The time a user spends on the website follows a gamma distribution. Which of these is NOT a suitable use of the gamma distribution in this scenario?
Predicting the time until a user makes a purchase.
Modeling the total time users spend on specific pages.
Analyzing the distribution of session durations.
Estimating the probability of a user clicking on an advertisement.
The heights of adult males in a certain population are normally distributed with a mean of 175 cm and a standard deviation of 7 cm. What percentage of men are taller than 189 cm?
16%
2.5%
5%
32%
A machine produces widgets with a defect rate of 5%. What is the probability that a batch of 20 widgets will contain exactly 2 defective ones?
0.1887
0.0025
0.9975
0.8113
You are simulating a random process with a known theoretical mean. After many simulations, you find that the average of your simulated results is significantly different from the expected theoretical mean. What is the MOST likely explanation for this discrepancy?
There is an error in your simulation code or methodology.
You have not run enough simulations for the Law of Large Numbers to take effect.
The theoretical mean is incorrect.
The Law of Large Numbers does not apply to simulations.