Free Access PRMIA.8007.v2022-03-05.q43 Practice Test (Page 5)

Question 16

The gradient of a smooth function is

A.a matrix containing the function's second partial derivatives

B.matrix of second partial derivatives of a function

C.a vector that shows the direction of fastest change of a function

D.infinite at a maximum point

Question 17

Which of the following can induce a 'multicollinearity' problem in a regression model?

A.A high positive correlation between two explanatory variables

B.A high positive correlation between the dependent variable and one of the explanatory variables

C.A large negative correlation between the dependent variable and one of the explanatory variables

D.The omission of a relevant explanatory variable

Question 18

Concerning a standard normal distribution and a Student's t distribution (with more than four degrees of freedom), which of the following is true?

A.The normal distribution has higher kurtosis than the t distribution.

B.The normal distribution has lower kurtosis than the t distribution.

C.Which has the higher kurtosis depends on the degrees of freedom of the t distribution.

D.The distributions have the same kurtosis.

Question 19

The Lagrangian of a constrained optimisation problem is given by L(x,y,) = 16x+8x2+4y-(4x+y-20), where is the Lagrange multiplier. What is the solution for x and y?

A.x = 5, y = 0

B.x = 0, y = 20

C.None of the above

D.x = -1, y = 0

Question 20

You want to test the hypothesis that a population parameter of a regression model is zero. Your alternative hypothesis is that 0. Denote by SD() the estimated standard deviation of , and by MEAN() the estimated mean of . Which test statistic is appropriate, and what is its distribution?

A.test statistic = MEAN()/SD(), normal distribution

B.test statistic = SD()/MEAN(), normal distribution

C.test statistic = SD()/MEAN(), t distribution

D.test statistic = MEAN()/SD(), t distribution

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