Explanation

Probability refers to the likelihood of a single event or outcome occurring, not a collection of experiments.

Explanation

• A Type-II error means accepting an incorrect hypothesis (or failing to reject a false null hypothesis).
• This means that the test or experiment has failed to detect a significant effect or difference when it actually exists.

Explanation

Since X is a uniform variate between 0 and 3, the probability density function (pdf) of X is:

f(x) = 1/3 for 0 ≤ x ≤ 3

To find E(X²), we need to calculate the expected value of X², which is:

E(X²) = ∫x²f(x)dx = ∫(x²/3)dx from 0 to 3

Evaluating the integral, we get:

E(X²) = (1/3)∫x²dx from 0 to 3 = (1/3)[(3³)/3] = 3

So, the expected value of X² is 3.

Explanation

• The Second Quartile (Q2) is a measure of central tendency, also known as the median.
• It is the middle value of a dataset when it is sorted in order.

Explanation

In the presence of multicollinearity, the OLS estimator will still be consistent unbiased and efficient.

Explanation

• Simple correlation, also known as Pearson's r.
• It is a statistical technique used to measure the strength and direction of the linear relationship between two continuous variables, X and Y.
• It is called "simple" because it involves only two variables.

Explanation

• The coefficient of correlation (ρ) is a measure of the linear relationship between two variables.
• It is a dimensionless quantity, which means that it is unaffected by changes in the scale or units of the variables.

Explanation

Design of experiments (DOE) is commonly used to:

• Develop new processes
• Improve existing processes
• Optimize process parameters
• Reduce variability
• Improve product quality

Explanation

• Multiple regression is a statistical technique that examines the relationship between a dependent variable (outcome variable) and two or more independent variables (predictor variables).
• It helps to predict the value of the dependent variable based on the values of the independent variables.

Explanation

A confidence level of 95% corresponds to a significance level of 0.05.

The significance level, often denoted by alpha (α), is the probability of rejecting the null hypothesis when it is true.

 It is the complement of the confidence level.

 Therefore, if the confidence level is 95%, the significance level would be

1- 0.95 = 0.05