Chapter 5 - Probability

Question 1

Conditional Probability

Answer 1

Probability of a certain thing given another certain thing

Book example 1 –> P(9 year old | girl) –> probability of being a 9 year old in the subcategory of girls

Question 2

Sensitivity and Specificity

Answer 2

Sensitivity, or true positive fraction = probability that a diseased person screen positive
P(screen positive | disease)

Specificity, or true negative fraction = probability that a disease free person screens negative
P(screen negative | disease free)

Question 3

False positive fraction vs. False negative fraction

Answer 3

False positive fraction = 1 - specificity
P(screen positive | disease free)

False negative fraction = 1 - sensitivity
P(screen negative | disease)

Question 4

Positive and negative predictive value

Answer 4

Positive predictive value - probability that if I have the disease, the test will come back positive
P(disease | screen positive)

Negative predictive value - probability that if I don’t have the disease, test will come back negative

Question 5

Independent events

Answer 5

occurrence of one event is not affected by the occurrence or non-occurrence of another event

      P(A | B) = P(A)          OR          P(B | A) = P(B)

Question 6

Bayes’ Theorem

Answer 6

Probability rule that is used to compute conditional probability based on specific available information
See Page 74 for equation

Question 7

Complementary Events

Answer 7

probabilities of complementary events sum to 1

Question 8

Binomial distribution

Answer 8

probability distribution for experiments/processes have 2 outcomes

 must clearly specify which outcome is the "success" and which outcome is the "failure," even if the negative outcome is the success

      See page 75 for equation

appropriate use must satisfy three assumptions:

1) only two outcomes
2) probability of success is the same for both outcomes
3) probabilities of success and failure are independent

Question 9

Binomial mean number of successes and standard deviation

Answer 9

Mean = mu = np

standard deviation = little sigma = sqrt(n(p)(1 - p))

Question 10

The Normal distro

Answer 10

appropriate when an experiment or process results in a continuous outcome

Gaussian distro

Assumptions

1) Mean = median = mode
2) ~68% of population values fall between one std dev above and below the mean
3) ~95% of population values fall between two std devs above and below the mean
4) ~99.9% of population values fall between three std devs above and below the mean
5) symmetric about the mean

      see page 79 for equation - needs calculus o\_\_O

for any probability distibution, total area under the curve is 1

Question 11

Probability of a Characteristic

Answer 11

(Number of people with a characteristic)/(Number of people in the population)