Question

∑ i=1

n
​
(ax i
​
+by i
​
+c)= A. a x
ˉ
+b y
ˉ
​
+n×c. B. a∑ i=1
n
​
x i
​
+b∑ i=1
n
​
y i
​
+n×c. C. a∑ i=1
n
​
x i
​
+b∑ i=1
n
​
y i
​
D. a∑ i=1
n
​
x i
​
+b∑ i=1
n
​
y i
​
+c Consider the following linear transformation of a random variable y= σ x
​
x−μ x
​
​
, where μ x
​
is the mean of x and σ x
​
is the standard deviation. Then the expected value and the standard deviation of are given as: A. 0 and 1 . B. cannot be computed because Y is not a linear function of X. C. σ x
​
μ x
​
​
and σ x
​
. D. 1 and 1 . 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: A. 3.5. B. 3.0. C. 3.25. D. 2.78. For a normal distribution, the skewness and kurtosis measures are as follows: A. 0 and 0 . B. 1 and 2 . C. 0 and 3 . D. 1.96 and 4 .

Answer 1

First question cut off,

Regarding the second question, the transformation of a random variable is given as:

y = σ(x - μ)/σ

where μ is the mean of x and σ is the standard deviation of x.

The expected value of this transformation can be calculated as:

E(y) = E[σ(x - μ)/σ] = (σ/σ)E(x - μ) = E(x) - μ

Therefore, the expected value of the transformed variable y is μ. The standard deviation of the transformed variable y remains the same as the standard deviation of x, which is σ.

So, the expected value of the transformed variable is μ and the standard deviation is σ. The correct answer is A. 0 and 1.

For the third question, the expected value of your final grade depends on the subjective probabilities assigned to each grade. Since the probabilities are not provided, it is not possible to determine the expected value.

For the fourth question, a normal distribution has a skewness of 0 and a kurtosis of 3. Therefore, the correct answer is C. 0 and 3.