1st lecture

Question 1

Probability Distribution

Answer 1

tells us the probabilities of observing different values within a population

Question 2

pdf

Answer 2

the probability density function is the function displaying the probability distribution

Question 3

Discrete RV

Answer 3

can take on only certain specific values

Question 4

Continuous RV

Answer 4

can take any value

the probability that a continuous RV will take on a specific value is always zero

probabilities for continuous values are described by pdf’s

Question 5

Measures of Central Tendency

Answer 5

median
mean
mode

Question 6

Variance

Answer 6

measures the dispersion of a probability distribution

Question 7

Range

Answer 7

difference between the largest and smallest of the observed data points

Question 8

Interquartile range

Answer 8

difference between the 75th and 25th percentile

Question 9

Covariance & Correlation

Answer 9

Covariance shows the direction in which both variables move;
Correlation shows the direction AND the strength in which two different variables move

Question 10

Cov(x,y) = 0

Answer 10

both variables are independent from each other

Question 11

E[X x Y] = …

Answer 11

E[X] x E[Y] + cov(X,Y)

Question 12

Var(Zahl)=

Answer 12

0

Question 13

Var(cY+d) = …

Answer 13

c²Var(y)

Question 14

Var(cX+dY) = …

Answer 14

c²Var(X) + d²Var(Y) +2cdCov(X,Y)

Question 15

Cov(x+y , z) = …

Answer 15

cov(x,z) + cov(y,z)

Question 16

What is the meaning of “unimodal”?

Answer 16

Only one peak in the distribution

Question 17

Standard normally distributed variable:

Answer 17

Z = (y-mean) / stdev

Question 18

Cumulative distribution function

Answer 18

The probability that a continuous RV lies above or below a certain value

Question 19

X²- distribution

Answer 19

sum of squares of n independent standard normal distributions wit h degrees of freedom

Question 20

Degrees of freedom - …

Answer 20

Number of independent values that can vary in an analysis without breaking any constraints (observations - parameters)

Question 21

F - distribution: F(n1,n2)

Answer 21

the ratio of two independent X² distributions divided by their respective degrees of freedom n1 and n2

Question 22

CLT - central limit theorem:

Answer 22

allows us to make inferences about a whole population using sample data, regardless of the population’s original distribution.
Taking many samples of a population and calculating their means will result in a normal sample mean distribution, although the original distribution wasn’t normally distributed.

Question 23

What does a regression do?

Answer 23

it describes and evaluates the empirical relationship between dependent and independent variables using a sample of data