Platykurtic.
Leptokurtic.
Normal distribution
This distribution has different kurtosis with normal distribution, but we cannot
judge by neasure of kurtosis directly
On a 12-question multiple-choice test, there are four possible answers for each
question, of which one is correct. Suppose that a student guesses on each question. Let
X equal the number of correct answers. What is E(X ) ? (3%)
3
6
9
10
Bowl B1 contains two red and five white chips, and bowl B2 contains four red and
three chips. A fir die is cast. If the output is a multiple of 3 (namely, 3 or 6), a chip is
taken from bowl B2 ; Otherwise a chip is taken from bowl B1 . Given that the selected
chip is red, what is the conditional probability that it was taken from bowl B1 . (3%)
8/21
1/3
1/2
10/21
If X is normally distributed with a mean of 6 and a variance of 25. What is
P(| X − 6 | < 5) ? (3%)
0.65
0.9544
0.5403
0.6826
Let X have a Poisson distribution with a mean of 4. What is P(2 ≤ X ≤ 5) ? (3%)
0.532
0.693
0.65
0.477
If Z is a random variable that is t distribution with T −1 degree of freedom, which
distribution W = Z 2 converge to? (3%)
χ 2 (T −1)
t(T −1)
N(0, T −1)
F(1, T −1)
If it is known that X has a mean of 33 and a variance of 16, then, which is the upper
bound for P(| X − 33 | ≥ 14) ? (3%)
0.71
0.89
.084
0.92
The conditional distribution of Y given X = x , Pr(Y = y | X = x) , is (3%)
Estimation of the IV regression model (3%)
requires exact identification
allows only one endogenous regressor, which is typically correlated with the error
term.
requires exact identification or overidentification
is only possible if the number of instruments is the same as the number of
regressors
The distinction between endogenous and exogenous variables is (3%)
that exogenous variables are determined inside the model and endogenous variables
are determined outside the model
dependent on the sample size: for n > 100 , endogenous variables become
exogenous
depends on the distribution of the variables: when they are normally distributed,
they are exogenous, otherwise they are endogenous
whether or not the variables are correlated with the error term
The AR( p) model (3%)
represents Yt as a linear function of p of its lagged values.
The confidence interval for the sample regression function slope (3%)
can be used to conduct a test about a hypothesized population regression function
slope
can be used to compare the value of the slope relative to that of the intercept
adds and subtracts 1.96 from the slope
allows you to make statements about the economic importance of your estimate.
Under the least squares assumptions (zero conditional mean for the error term, Xi
and Yi being i.i.d., and Xi and ui having finite fourth moments), the OLS
estimator for the slope and intercept (3%)
has an exact normal distribution for n > 15 .
is BLUE
has a normal distribution even in small samples
is unbiased
Imagine you regressed earnings of individuals on a constant, a binary variable (“Male”)
which takes on the value 1 for males and is 0 otherwise, and another binary variable
(“Female”) which takes on the value 1 for females and is 0 otherwise. Because females
typically earn less than males, you would expect (3%)
the coefficient for Male to have a positive sign, and for Female a negative sign
both coefficients to be the same distance from the constant, one above and the other
below.
none of the OLS estimators to exist because there is perfect multicollinearity
this to yield a difference in means statistic
When you have an omitted variable problem, the assumption that E(ui | Xi ) = 0 is
violated. This implies that (3%)
the sum of the residuals is no longer zero
there is another estimator called weighted least squares, which is BLUE
the sum of the residuals times any of the explanatory variables is no longer zero
the OLS estimator is no longer consistent
it has a smaller variance.
its c.d.f. is flatter than that of the other estimator.
(一) Why we employ the normality assumption in classical linear regression model?
What is the Central Limit Theorem? (10%)
(二) What is the type I error? What is the type II error? Can we minimize both the errors
simultaneously? (10%)
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)