Explanation

• Regression analysis is a statistical technique used to establish a relationship between two variables (independent and dependent) to predict the value of one variable based on the other.
• It helps in building a prediction model that can forecast the outcome.

Explanation

• When several unbiased samples are drawn from the same population, the sampling technique is Random Sampling.
• In random sampling, each member of the population has an equal chance of being selected, and the samples are drawn independently.
• This allows for the calculation of sampling distributions and the estimation of population parameters.

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

• In the Cramér-Rao inequality, var(T) is the minimum variance bound, which represents the lowest possible variance of an unbiased estimator T.
• This bound is a fundamental limit in estimation theory and is used to evaluate the efficiency of estimators.

Explanation

Origin lies on the intersection of the x-axis and y-axis, i.e. (0,0).

Explanation

In a histogram, the Y-axis represents the frequencies (i.e., how many data points fall into each class).

The X-axis shows the class intervals (data ranges).

Explanation

Both statements are factually true, so the conjunction p ∧ q is true.

Explanation

The product of the first 'n' natural numbers is represented by the formula:

n! (n factorial) = 1 × 2 × 3 × ... × (n-2) × (n-1) × n

This is denoted by the symbol "n!" and is read as "n factorial".

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

Two events A and B are independent if the occurrence of one does not affect the occurrence of the other.

This is mathematically defined as:

  P(A ∩ B) = P(A) × P(B)