Discrete random variables

Question 1

When can we combine two variables for expectation and variance?

Answer 1

Expectation when the two variables are random.Variance when they are random and independent.

Question 2

Assumptions for binomial distribution?

Answer 2

Trials are independent
Each trial results in success or failure
Probability of success is constant for each trial
N is a fixed number of trials.

Question 3

Assumptions of a poisson distrbution?

Answer 3

Events occur at a constant average rate
Lambda represents the mean number of events occurring in a given interval of time or space.
Trials are random and independent of each other.
Events occur singly.

Question 4

What is the poisson distribution used for?What type of distribution is it?

Answer 4

It is used to find the mean number of events occurring in a given interval or space.It is a infinite distribution

Question 5

How to combine two variables X and Y which follow the poisson distribution.

Answer 5

Let T=x+y

T follows a poisson distribution with parameter lambda t=lambda x+lambda y.

Question 6

What are the conditions for the geo distribution and whats the formula?

Answer 6

It is used to find the number of trials up to and including the first success.
Trials must be independent
Probability of success is constant for each trial
Each trial can be classified as a success or failure.

Question 7

What is the value of P(X>r) for the geo distribution?

Answer 7

q^r.

Question 8

When is it appropiate to use PMCC hypothesis test?

Answer 8

When the data is drawn from an bivariate approximate normal distribution.