Discrete Probability Distributions

Question 1

What is a random variable

Answer 1

A variable that summarizes the result of the experiment in numerical values

Question 2

Why can’t you describe a continuous random variable as a list of x’s

Answer 2

Because continuous means that it can take any variable, that the numbers of alternatives are not countable. Only discrete, random variables can be described this way.

Question 3

What are the two key properties of discrete probability distributions?

Answer 3

The probability of each x is between zero and one, and the sum of probabilities equals one.

Question 4

What is a cumulative, probability distribution

Answer 4

The cumulative probability distribution shows the likelihood of getting the index or in the index below it

Question 5

What is the probability distribution of a discrete, random variable?

Answer 5

The likelihood of each alternative that the variable can have

Question 6

P(X=x)={2 if x=1,2,3 1 otherwise }
a P(X=2)
b P(X=8)

Answer 6

a 2
b 1

Question 7

What are the characteristic of a discrete uniform distribution in probability?

Answer 7

equal likelihood between alternatives and a symmetric distribution of likelihood between alternatives

Question 8

What is the expected value of a discrete, random variable

Answer 8

The weighted average of all alternatives. They alternative weighted by its probability.

Question 9

What is the expected return of two assets E(X+Y)

Answer 9

The sum of the expected return of each asset. The assets are also be waited accordingly.

Question 10

What is the variance of two assets?

Answer 10

The sum of the variance of each asset, in addition to twice the covariance of the two assets together

Question 11

When can one asset in the portfolio contract the other asset

Answer 11

When the assets are not correlated enough

Question 12

What is an Bernoulli process?

Answer 12

A series of identical trials of an experiment, such that on each trial, there are only two possible outcomes, success and failure, and the probabilities of success and failure remain the same from trial to trial

Question 13

What is in a binomial random variable

Answer 13

The number of successes in the n’th trial of the Bernoullian process

Question 14

What is the binomial probability distribution?

Answer 14

Binominal distribution is the likelihood of a biniminal, random variable to have each of its potential values

Question 15

What is the binomial coefficient?

Answer 15

The number of sequences possible that can play out in the Bernoulli process calculated by the factorial combination formula, when the order does not matter

Question 16

When is the poisson distribution used?

Answer 16

When you want to find the number of occurrences of a certain event over time and space

Question 17

When can you use the poisson process?

Answer 17

The number of the successes are counted as integers, the probability of success is proportional to the size of the interval, the interval valves don’t overlap, and the successes are independent

Question 18

What is the mean of a poison, random variable equal to

Answer 18

It’s variance

Question 19

When should we use hypergeometric distribution?

Answer 19

When we cannot assume the trials are independent in the Bernoulli process. Suggest the likelihood of trying a winning tickets out of subsequent drawings from a bowl.