Explanation

The correct statement regarding the coefficient of correlation is: It is independent of both the scale and origin.

Explanation

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

Explanation

There are 12 face cards in a standard deck of 52 cards (3 face cards per suit x 4 suits).

The probability of drawing 2 face cards is: C(12,2) x C(40,3) / C(52,5) = 0.0533

Explanation

Explanation

• Two mutually exclusive events are dependent.
  
• If one event occurs, it completely affects the occurrence of the other, meaning the other event cannot occur, which makes them dependent in this context.

Explanation

• The variance of a Poisson distribution is equal to its mean, which is denoted by m.
• This means that if a random variable X follows a Poisson distribution with mean m, then the variance of X is also m.

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

The harmonic mean is the appropriate measure of central tendency to use when calculating the average speed of a journey.

This is because speed is a rate (distance per unit time), and the harmonic mean is used to average rates.

The formula for harmonic mean is: H = n / (∑(1/x))

where H is the harmonic mean, n is the number of values, and x is each value.

Explanation

• The alternate hypothesis is also known as the alternative hypothesis.
• It determines whether a test is one-tailed or two-tailed.

Explanation

• The Rao-Blackwell theorem enables us to obtain minimum variance unbiased estimates through sufficient statistics, which capture all the information in the data about the parameter.
• By conditioning an unbiased estimator on a sufficient statistic, we can improve its precision and obtain the minimum variance unbiased estimator (MVUE).