Statistics - Distributions

Question 1

What is P(X = x)?

Answer 1

Probability of random variable X takes the value x

Question 2

What is a random variable?

Answer 2

Variable whose value depends on the outcome of a random events
Showed by capital letter e.g X or Y

Question 3

How can you write the sum of all probabilities?

Answer 3

Sum of P(X = x) = 1

Question 4

What is a discrete random variable?

Answer 4

A value which can take a certain number of different values with different probabilities

Question 5

What is a probability distribution?

Answer 5

A table which shows all possible values it can take and the probability that it takes each value

Question 6

What is the notation for a discrete random variable?

Answer 6

X (uppercase)

Question 7

What is the notation for particular values that X can be represented by?

Answer 7

x (lowercase)

Question 8

What is a probability function?

Answer 8

Formula that generates the probability of X taking the value x
Written as P(X=x)

Question 9

What is the cumulative distribution function?

Answer 9

Probability that X will be less than or equal to a particular value of x

Question 10

How is the cumulative distribution function calculated?

Answer 10

Add up all of the values X can take which are less than or equal to the value of x

Question 11

How many orders can things be if some are the same?

Answer 11

n objects, of which x are identical

Arranged in n!/x!

Question 12

When does a random variable X follow a binomial distribution?

Answer 12

Fixed number of (n) trials
Each trial involves either success or failure
All trials are independent
Probability of success is the same in each trial
The variable is the total number of successes in n trials

Question 13

How can a binomial distribution be written with X?

Answer 13

X~B(n,p)
X - random variable
n - number of trials
p - probability of “success”

Question 14

How would you approach P( 3 <= X <= 5)?

Answer 14

P( 3 <= X <= 5) = P(X<=5) - P(X<=2)

Question 15

How would you approach P(X<7) ?

Answer 15

P(X<7) = P(X<=6)

Question 16

How would you approach P(X>=7)?

Answer 16

1 - P(X<=6)

Question 17

How would you approach P(X>6)?

Answer 17

P(X>6) = 1 - P(X<=6)

Question 18

How do you use the calculator with the binomial distribution X~B(n,p)?

Answer 18

Set values:
x = number of the trial
n = number of trials
p = probability of “success”

Question 19

What is E(X)?

Answer 19

Mean or expected value

E(X) = np

Question 20

What should be looked for if you are finding the minimum value of b that P(X>=b) < 0.05?

Answer 20

P(X>=b) < 0.05 = P(X<=b) > 0.95

Question 21

What is the variance of a binomial distribution?

Answer 21

Variance = np(1-p)
n = number of tests
p = probability of "success"