180 câu trắc nghiệm Kinh tế lượng – Phần 1

Chapter 2: Review of Probability

KTL_001_C2_1: The expected value of a discrete random variable
○ is the outcome that is most likely to occur.
○ can be found by determining the 50% value in the c.d.f.
○ equals the population median.
● is computed as a weighted average of the possible outcome of that random variable, where the weights are the probabilities of that outcome.

KTL_001_C2_2: For a normal distribution, the skewness and kurtosis measures are as follows:
○ 1.96 and 4
○ 0 and 0
● 0 and 3
○ 1 and 2

KTL_001_C2_3: The correlation between X and Y
○ cannot be negative since variances are always positive.
○ is the covariance squared.
● can be calculated by dividing the covariance between X and Y by the product of the two standard deviations.
○ is given by \(corr(X,Y) = \frac{{{{\rm cov}} (X,Y)}}{{var(X){{\rm var}} (Y)}}\)

KTL_001_C2_4: Assume that Y is normally distributed \(N(\mu ,{\sigma ^2})\). Moving from the mean (\(\mu \)) 1.96 standard deviations to the left and 1.96 standard deviations to the right, then the area under the normal p.d.f is
○ 0.67
○ 0.05
● 0.95
○ 0.33

KTL_001_C2_5: The variance of \(\bar Y,\begin{array}{ccccccccccccccc}{}&{\sigma _{\bar Y}^2}\end{array}\), is given by the following formula:
○ \({\sigma _Y^2}\).
○ \(\frac{{{\sigma _Y}}}{{\sqrt n }}\)
● \(\frac{{\sigma _Y^2}}{n}\).
○ \(\frac{{\sigma _Y^2}}{{\sqrt n }}\)

KTL_001_C2_6: \(\sum\limits_{i = 1}^n {\left( {a{x_i} + b{y_i} + c} \right)} = \)
○
● \(a\sum\limits_{i = 1}^n {{x_i}} + b\sum\limits_{i = 1}^n {{y_i}} + n*c\)
○ \(a\sum\limits_{i = 1}^n {{x_i}} + b\sum\limits_{i = 1}^n {{y_i}} + c\)
○
○ \(a\bar x + b\bar y + n*c\)
○
○ \(a\sum\limits_{i = 1}^n {{x_i}} + b\sum\limits_{i = 1}^n {{y_i}} \)
○

KTL_001_C2_7: \(\sum\limits_{i = 1}^n {\left( {a{x_i} + b} \right)} = \)
○ n*(a+b)
● \(n*a\bar x + n*b\)
○ \(\bar x + n*b\)
○ \(n*a*\bar x\)

KTL_001_C2_8: Assume that you assign the following subjective probabilities for your final grade in your econometrics course (the standard GPA scale of 4 = A to 0 = F applies):

The expected value is:
○ 3.0
○ 3.5
● 2.78
○ 3.25

KTL_001_C2_9: The mean and variance of a Bernoulli random variable are given as
○ cannot be calculated
○ np and np(1-p)
○ p and \(p\sqrt {(1 – p)} \)
● p and (1-p)

KTL_001_C2_10: Consider the following linear transformation of a random variable \(y = \frac{{x – {\mu _x}}}{{{\sigma _x}}}\), where \({{\mu _x}}\) is the mean of x and \({{\sigma _x}}\) is the standard deviation. Then the expected value and the standard deviation of Y are given as
● 0 and 1
○ 1 and 1
○ Cannot be computed because Y is not a linear function of X
○ \(\frac{{{\mu _x}}}{{{\sigma _x}}}\) and \({{\sigma _x}}\)

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