Probability Theory And Probability Distributions

Question 1

Review what do histograms show vs bar charts

Answer 1

For categorical values , bar charts show what proportion of the sample have a certain value
For quantitative variables , histograms show what proportion of sample have a certain value

Question 2

Probability distribution

Answer 2

Applies theory of probability to describe behavior of the random variable

Question 3

Random variables and types

Answer 3

Variable whose value is an outcome of a random phenomenon.
Continuous random variable can take on any value within specified interval ie weight
Discrete random variable can only assume finite or countable number of outcomes ie marital status ( single, married , divorced )

Question 4

Probability

Answer 4

Of a random value is the proportion of times that occurs in the population

Question 5

What does discrete random variable specify

Answer 5

It specifies all possible outcomes of the random variable along with probability that each will occur ie flipping a coin

Question 6

For continuous random variables

Answer 6

Allows us to determine the probabilities associated with specified ranges of values

Question 7

Things to note

Answer 7

A probability distribution can be thought of as a bar chart or histogram of the entire population

Question 8

Rules of probability

Answer 8

1. Probability must be between 0 & 1
2. Sum of probabilities for all possible mutually exclusive events must equal 1
3. P(not E)= 1-P(E)
4. Additive rule of probability P( A or B)= P(A) + P(B)
5. Multiplicative rule for independent events P(A & B) = P(A) *P(B)

Question 9

Discrete probability distribution X

Answer 9

Lists all possible values of X and their probabilities

Question 10

Continuous probability distribution of X

Answer 10

Summarize all possible values of X and their probabilities using probability density curve
Only use density curve if it provides good fit to our data
Can have variable shapes

Question 11

Properties of probability density curves

Answer 11

Vertical scale - probability 0-1
Area under curve is equal to 1 ( because the area represents the sum of probabilities for all possible values of the variable
For continuous random variable , we do not talk about probability of an individual value rather the probability that the value lies within intervals

Question 12

Normal distribution

Answer 12

Model for continuous data, need population mean and population sd to define a unique normal distribution

Question 13

Properties of normal distribution

Answer 13

Takes values between positive infinity and negative infinity
Area under curve equals 1
Symmetric around mean . mean=median=mode
Examples; blood pressure , age , Hb

Question 14

What does X~ N(mean, variance squared mean)

Answer 14

X is normally distributed with mean and variance squared

Question 15

How does sd and mean affect shape of the graph

Answer 15

For sd causes the height to change
For means causes the graph shift to left or right

Question 16

Standard normal distribution

Answer 16

Normal distribution with population mean mu =0 and standard deviation, sigma =1

Question 17

How is standardizing of data done?

Answer 17

For each X value we calculate new Z value known as Z score

Question 18

Formula for Z Score, what is Z score

Answer 18

Measures number of sd that data point X is from mean mu

Question 19

Binomial distribution

Answer 19

Probability distribution for binomia experiment used with discrete data . Referred to probability of getting n successes in a specific number of trials

Question 20

Bernoulli trial

Answer 20

Experiment where there are only 2 possible outcomes , the probability of success 0, is constant from trial to trial , so trials are independent

Question 21

What is the probability of getting 2 heads after tossing coin 5 times

Answer 21

10

Question 22

Assumptions for binomial distribution

Answer 22

Number of observation is fixies
There are only 2 outcomes
Each observation is independent
Probability of success p is constant from trial to trial