4 Introduction to Probability Distributions

Question 1

What is the formula for the mean of a discrete random variable?

Answer 1

Question 2

What is the definition of a discrete random variable?

Answer 2

A discrete random variable is an event or set of events which has a limited number of possible outcomes.

Question 3

What defines discrete data?

Answer 3

Data is defined as DISCRETE if it can only take certain values.

Question 4

What is a random variable?

Answer 4

A random variable is one which depends on random events – that is the event is unpredictable.

Question 5

What is the expected value in probability distributions?

Answer 5

The expected value can be considered the mean of a probability distribution.

Question 6

What is variance in the context of probability distributions?

Answer 6

Question 7

Define a uniform distribution.

Answer 7

A uniform distribution is a random variable which has a constant probability and is symmetrical.

Question 8

What is the formula for the expected value of a continuous uniform distribution?

Answer 8

where a and b are the bounds of the distribution.

Question 9

True or False: Continuous random variables can take any value within a given range.

Answer 9

True.

Question 10

Define a continuous uniform distribution.

Answer 10

A continuous uniform distribution is a continuous random variable which has a constant probability and is symmetrical.

Question 11

Define a discrete uniform distribution.

Answer 11

A discrete uniform distribution is a random variable in which each outcome has the same probability.

Question 12

What is the significance of the notation P(X=x)?

Answer 12

It represents the probability that the random variable X takes the value x.

Question 13

What is the relationship between probability and expectation?

Answer 13

Expectation is calculated using probabilities of the outcomes of a random variable.

Question 14

What does the term ‘mean’ refer to in probability distributions?

Answer 14

The average value of the outcomes, also known as the expected value.

Question 15

What is the formula for the variance of a continuous uniform distribution?

Answer 15

where a and b are the bounds of the distribution

Question 16

Fill in the blank: The probability of an event occurring is expressed as a _______.

Answer 16

[number between 0 and 1]

Question 17

What is the expected outcome for a discrete random variable?

Answer 17

It can be calculated using the probabilities and the values of the random variable.

Question 18

What does it mean for a distribution to be symmetrical?

Answer 18

Mean=Median

Question 19

Fill in the blank: The mean is also referred to as the _______.

Answer 19

[expected value]

Question 20

What is the significance of the ‘at least’ and ‘at most’ terms in probability?

Answer 20

They help define the range of outcomes that are considered in probability calculations.

Question 21

For any continuous random variable, what is P(X=x)?

Answer 21

0