Final Module (4 & 5)

Question 1

Discreet random variable

Answer 1

a random variable that can take on a finite or countable number of values

Question 2

Continuous random variable

Answer 2

a random variable whose values lie in a continuous interval

Question 3

Distribution function

Answer 3

a function that matches the value of a random variable to the probability of the corresponding outcome

Question 4

Distribution function of a discreet RV is called

Answer 4

Probability Mass Function (PMF)

Question 5

Distribution function of a continuous RV is called

Answer 5

Probability Density Function (PDF)

Question 6

Cumulative Distribution Function

Answer 6

the probability that the value of a random variable is less than the specified number

Question 7

Normal Distribution, percentage to sigma

Answer 7

within mu = 34.1%
mu + std = 13.6 %
mu + 2std = 2.1 %
mu + 3std = 0.1%
——-
within mu = 68.2 %
mu +- std = 95.4 %
mu +- 2std = 99.6 %
mu +- 3std = 99.8 %

Question 8

Poisson distribution

Answer 8

associated with counting and provides the probability of a given number of events in a fixed period of time

Question 9

Lognormal Distribution

Answer 9

distribution of a random variable whose logarithm is normally distributed

Question 10

Lognormal Distribution examples

Answer 10

• Stock returns
• Weight and blood pressure of humans
• Survival time of bacteria in antiseptics

Question 11

Binomial distribution

Answer 11

gives the probability of k successes in n trials where the probability of each success is p

Question 12

Interquartile range

Answer 12

the range of the middle half of the distribution

Question 13

Measures of variation

Answer 13

are characteristics of distribution that show how far apart the data points are from each other or how spread the distribution is

Question 14

Variance & Standard deviation

Answer 14

average of the squared distances from the mean
- Standard deviation – square root of the variance

Question 15

Volatility

Answer 15

the standard deviation of the return

Question 16

Skewness

Answer 16

measures how symmetrical the distribution is around the mean

Question 17

Kurtosis

Answer 17

shows how widely spread the distribution is (similar to the variance)

Question 18

Positive skew v.s. Negative skew

Answer 18

Positive skew:
mean > median

Negative skew:
mean < median

Question 19

Notation: 𝑋~𝑁(𝜇, 𝜎2) means

Answer 19

random variable 𝑋 is drawn from a normal distribution with mean 𝜇 and standard deviation 𝜎

Question 20

Standard Normal Distribution

Answer 20

normal distribution with the mean of 0 and standard deviation of 1 - Notation: 𝑋~𝑁(𝜇, 𝜎2)