The lifetime of a certain electronic component follows an exponential distribution with a mean of 10,000 hours. What is the probability that a randomly selected component lasts less than 5,000 hours?
0.6321
0.25
0.5
0.3935
Principal Component Analysis (PCA) is primarily a ______ technique.
Regression
Dimensionality Reduction
Clustering
Classification
You're playing a game where you flip a coin. Heads, you win $10. Tails, you lose $5. What is the expected value of playing this game?
$2.50
$0.00
$5.00
-$2.50
In a binomial distribution, if the probability of success on each trial is 0.3 and there are 10 trials, what is the expected value of the number of successes?
7
10
3
5
What pattern in residual analysis might suggest that a linear model is not appropriate for the data?
Residuals consistently increasing with increasing values of the independent variable
A curved pattern in the residuals
All residuals clustered around zero
Randomly scattered residuals
Which of the following sampling techniques is most likely to introduce bias?
Systematic sampling
Convenience sampling
Stratified random sampling
Simple random sampling
A coin is flipped 5 times. What is the probability of getting exactly 3 heads?
0.6875
0.3125
In residual analysis, what does a pattern in the residuals plot indicate?
The errors have constant variance.
There is no correlation between the variables.
The relationship between the variables may not be linear.
The linear model is a good fit for the data.
In simple linear regression, what does a negative slope of the regression line indicate?
There is no relationship between the independent and dependent variables.
The relationship between the independent and dependent variables is non-linear.
As the independent variable increases, the dependent variable increases.
As the independent variable increases, the dependent variable decreases.
Which of the following is NOT a key assumption of the Central Limit Theorem?
The samples are independent and randomly selected.
The population distribution is normal.
The population has a finite mean and variance.
The sample size is sufficiently large (generally n ≥ 30).