Probability, Odds and Binomial PMF

Question 1

What ranges must Proportions lie within?

Answer 1

0 to 1

Question 2

What ranges must Probabilities lie within?

Answer 2

0 to 1

Question 3

What does “the compliment of event F” mean?

Answer 3

The probability that event F does not occur

-Given by Pr(F bar)=1-Pr(f)

Question 4

What is probable intersection?

Answer 4

Is the event that both events F and G occur

-Pr(FnG)=Pr(F)/Pr(G)

Question 5

What is the Probable Union?

Answer 5

Is the event that either event F, G or both occur

-Pr(FUG)=Pr(F)+Pr(G)-Pr(FnG)

Question 6

What is mutually exclusive probability?

Answer 6

The event that Neither F not G can occur together

-Pr(FUG)=Pr(F)+Pr(G)

Question 7

What is probable independence?

Answer 7

The event in which two unrelated events occur

-Pr(FnG)=Pr(F)xPr(G)

Question 8

What is conditional Probability?

Answer 8

The event that F happens given G has occurred
-Pr(F|G)=Pr(FnG)/Pr(F)
If F and G are independent this simplifies to:
-Pr(F|G)=Pr(F)

Question 9

What is the Probability Mass Function?

Answer 9

• The PMF tells us everything we need to know about the properties of a random variable x
• Done by completing PMF tables

Question 10

Describe the Binomial distribution

Answer 10

• Binary outcomes are characterised by the binomial distribution
• Distribution has two parameters:
• number of fixed trials (n)
• Probability of success in a trail (p) (also fixed value)

Question 11

What does a small probability p value tell us?

Answer 11

There will be a small number of successes out of the number of trials conducted

Question 12

What does a large probability p value tell us?

Answer 12

There will be a large number of successes out of the number of trials conducted

Question 13

What are the four conditions of the Binomial distribution?

Answer 13

• Two outcomes
• Fixed number of trials
• Independence of of observations
• Constant probability of success

Question 14

Describe confidence intervals for proportions

Answer 14

• Similar of that too the CI of normal data except it is given by the Z distribution
• Z=1.96

Question 15

What will the estimate of a confidence interval of proportions be?

Answer 15

Usually within 2 standard errors of the P-value

Question 16

What is the hypothesises for proportional confidence intervals?

Answer 16

Ho: difference in proportions = 0
H1: difference in proportions is not = 0

Question 17

What sampling situation arises from proportions originating from independent samples?

Answer 17

Situation A

Question 18

What sampling situation arises from the same sample gives rise to two or more proportions where only one option can be chosen?

Answer 18

Situation B

Question 19

What sampling situation arises from the same sample gives rise to two or more proportions and there is no limit on the options that can be chosen?

Answer 19

Situation C

Question 20

What is the Value of Z ?

Answer 20

1.96

Question 21

What is an odd ratio?

Answer 21

The measure of effect which allows comparison of two results from a group (ie: comparison of control/placebo group)

Question 22

How is a statistical Odd calculated?

Answer 22

Odds = Pr(success)/Pr(failure)

Question 23

How is the confidence intervals for Odds ratios different to other CI’s?

Answer 23

You need to take the log of the ratio to start with

Question 24

How is an odds ratio calculated?

Answer 24

Odds ratio= odds(F)/odds(G)

-where the odds of F and G are the odds of success

Question 25

Whats is special about the value of odds?

Answer 25

They never take a negative value