Discrete Probability Distributions

Question 1

What are the conditions for binomial distribution?

Answer 1

FICT

Fixed number of trials
Independent trials
Constant probability of success
Two outcomes in each trial

Question 2

How can binomial distribution be denoted?

Answer 2

X ~ B(n,p)

Question 3

What is the formula for a binomial distribution?

Answer 3

P(X=x) = ⁿCx * p^x * (1-p)^n-x

Question 4

What is the formula for the mean of binomial distribution?

Answer 4

E(X) = np

Question 5

What is the formula for the variance of binomial distribution?

Answer 5

Var(X) = np(1-p)

Question 6

How do you calculate the most likely outcome?

Answer 6

The most likely outcome for X is the value of X which has the highest probability

Question 7

What is poisson distribution?

Answer 7

It is the probability distribution for the counting of events that occur randomly in a given time interval

Question 8

What are the conditions for poisson distribution?

Answer 8

Random occurrence of events
Independent events
Uniform average rate of occurrence

Question 9

How can Poisson distribution be denoted?

Answer 9

X ~ Po(y)

Question 10

What is the formula for Poisson distribution?

Answer 10

P(X=x) = (e^-y * y^x) /// x!

Question 11

What is the relationship between mean and variance in poisson distribution?

Answer 11

In poisson distribution, the mean and variance are almost equal. They both around about equal to the mean rate of occurrence or ‘y’

Question 12

What is the additive property of Poisson distributions?

Answer 12

X ~ Po(y₁)
W ~ Po(y₂)

X + W ~ Po(y₁ + y₂)

Question 13

What are the rules for cumulative probability calculations?

Answer 13

P(X < x) —> P(X _< x-1)

P(X > x) —> 1 - P(X _< x)

P(X >_ x) —> 1 - P(X _< x-1)

Question 14

What reason may binomial distribution not be possible?

Answer 14

If number of trials is large

Question 15

When can binomial distribution be approximated with poisson distribution?

Answer 15

Number of trials is large

Probability of success is small

Question 16

How does binomial distribution become poisson distribution?

Answer 16

B(n,p) —> Po(np)

Question 17

What is the general interval for when binomial distribution be approximated when poisson distribution?

Answer 17

When number of trials > 50

When probability of success < 0.1

Question 18

What words imply poisson distribution?

Answer 18

“Rate”
“Average number of occurrences”

Question 19

What words imply binomial distribution?

Answer 19

“Proportion”
“Probability of success”

Question 20

What is geometric distribution?

Answer 20

Geometric distribution calculates the number of trials required before success

Question 21

How is geometric distribution denoted?

Answer 21

P(X=x) = X ~ Geo(p)

Question 22

What is the formula for mean and variance for geometric distribution?

Answer 22

E(X) = 1/p

Var(X) = 1-p /// p²