True or False.

Are the following statements true or false? Explain your answers briefly. Without an

explanation the answer will be given zero points.

a. The total probability rule is used to determine how our subjective beliefs are modified

when we are confronted with new evidence.

b. A correlation coefficient close to zero indicates the lack of dependence between two

variables.

c. It is common to use lognormal distribution for modelling stock returns.

d. An estimator is unbiased if the probability of obtaining estimates close to the value

of the population parameter increases as sample size increases.

e. An increase in R2 after introducing a new explanatory variable does not say that the

new variable is statistically significant.

f. In a simple regression model y = b0 + b1x + u, let s denote the sample standard

deviation of the model's residuals, then the line of MATLAB code

s*sqrt(mean(x.^2)/sum((x-mean(x)).^2))

can be used to estimate the forecast error.