Topic 5 & 6

Question 1

a probability distribution of two random variables, 𝑋 and 𝑌 or their pair. These random variables may be either discrete or continuous

Answer 1

joint probability distribution

Question 2

referring to discrete random variables

Answer 2

Joint Probability Mass Function

Question 3

referring to continuous random variables

Answer 3

Joint Probability Density Function

Question 4

is the probability distribution of a subset of a collection of random variables, focusing on one variable at a time.

Answer 4

marginal distribution

Question 5

is the entire set of observations or elements that we are interested in studying

Answer 5

Population

Question 6

is a subset of the population selected for analysis.

Answer 6

Sample

Question 7

consistently overestimates or underestimates certain characteristics of the population, leading to inaccurate inferences

Answer 7

biased sampling procedure

Question 8

the process of using data from a sample to draw conclusions or make predictions about a population.

Answer 8

statistical inference

Question 9

eliminates any possibility of bias in the sampling procedure, ensuring that every elements of the population has an equal chance of being selected

Answer 9

Random Sample

Question 10

any function of the random sample/variable

Answer 10

statistic

Question 11

is a characteristic or measure that describes the entire population

Answer 11

parameter

Question 12

is the probability distribution of a statistic

Answer 12

sampling distribution

Question 13

states that if we take a sufficiently large sample size (𝑛) from a population with any distribution (whether finite or infinite), the sampling distribution of the sample mean (𝑋̅) will be approximately normal, with a mean (𝜇) and a variance of 𝜎^2 / 𝑛, provided that the sample size is large.

Answer 13

Central Limit Theorem (CLT)

Question 14

Common Sampling Distributions

Answer 14

1. t - distribution
2. F - distribution

Question 15

used extensively to estimate the population parameters but either have a small sample size or do not know the population’s standard deviation. It is similar to normal distribution
but has heavier tails, which accounts for the extra uncertainty when working with smaller samples.

Answer 15

t - distribution

Question 16

used when you want to compare the variances of two populations to see if they are significantly different.

Answer 16

F - distribution

Question 17

It is a principle that helps estimate unknown values about a population using the data from a sample

Answer 17

Point Estimation

Question 18

is a number or value that is in some sense a reasonable value (a good guess) of the true population parameter.

Answer 18

point estimate

Question 19

is a range of values, derived from sample data, that is likely to contain the true population parameter (such as the population mean or proportion).

Answer 19

confidence interval

Question 20

If the population standard deviation 𝜎 is known

Answer 20

we used the standard normal distribution (also
known as z-distribution). we use the t-distribution to account for the extra uncertainty introduced by using the sample standard deviation 𝑠.

Question 21

range of values the experimenter is interested in the possible value of future observations.

Answer 21

Prediction intervals