Probability distubritions of discrete data

Question 1

What are the 3 probability disturbtions for discrete data will we look at?

Answer 1

Uniform

Bernouli

Biniomial

Question 2

What is a discrete uniform distrbution and give an example?

Answer 2

Each value has the same probability of being observed.

Question 3

So what is the probabilitiy distrubtion of discrete uniform ?

Answer 3

Question 4

What is bernouli distubtion?

Answer 4

When there is 2 outcomes yes or no

e.g. For instance, a random person is asked if they support the Green party.

Question 5

What is the probability distrubtion of a bernouli distrbution?

Answer 5

Question 6

What is the expected value and variance of a bernouli distrbution?

Answer 6

Question 7

What is the probability distribution?

Answer 7

Question 8

What is binomial disturbtion?

Answer 8

This can be thought as the probabillity of a SUCESS or FAILURE outcome in an experiment repeated n times

Question 9

What is the Binominal distubtion of a random variable X?

Answer 9

Question 10

What is the probabiility of a binominal distrubtion with x sucess given a number of trials

Answer 10

Question 11

Lets say we have An operation with constant probability of success is carried out times, what can we calculate?

A known proportion, , of companies publish their gender pay structure. If we contact companies, what can we calculate?

Answer 11

We can calculate the probability of successful outcomes

what is the probability that out of publish it

Question 12

Explain the probabilitiy distrubtion of a biniomial distrubtion?

Answer 12

Question 13

What is this called and mean?

Answer 13

binomial coefficient

It gives the number of ways of selecting items from a set of ,where order is unimportant and no elements may be repeated.

Question 14

Calculate these binominal coefficients

Answer 14

Question 15

Necessary conditions to apply the binomial distribution are what?

Answer 15

Question 16

What is the expected value and variance of a binomial distubtion?

Answer 16

Question 17

Calculate expected value, variance and SD?

Answer 17

Question 18

Calculate expected value and variance, write the probability distubtion and binominal distubtion?

WRITE THE ASSUMPTIONS

Answer 18

Question 19

Calculate expected value and VAR wrtie distbtuion ?

not using the simple rule but previous rule to calculate expected value and var times probability by value of expected value?

Write the assumptions

Answer 19

Question 20

Calculate the expected value and variance, write the probability distrurbtion and the binominal distrubtion?

WRITE THE ASSUMPTIONS

Answer 20

Question 21

WRITE THE ASSUMPTIONS FIRST

Answer 21

Question 22

(LONG QUESTION)• An exam has 20 multiple choice questions, each with five possible answers; only one is correct.

• The probability a question is answered correctly by chance is 0.2.
• Find the probability that a student who guesses randomly at each answer obtains 0, 1, 2,…,20 correct answers.
• Determine where the pass mark should be set, so that a student who only guesses has probability less than 0.05 of exceeding the pass.

Answer 22

• Let = ‘the number of correct answers’. takes values from 0 to 20.

Question 23

Answer 23

Question 24

Answer 24

Question 25

Answer 25

Question 26

(Homework excerises) A certain electronic system contains 15 components. Suppose that the probability that each individual component will fail is 0.4 and that the components fail independently of each other. Given that at least two of the components have failed, what is the probability that at least three of the components have failed?

Answer 26

Question 27

The office of a large company has recently bought a consignment of 10 of the latest photocopying machines for use around the company. The office manager knows from previous experience that there is a 0.2 probability that any one machine will develop fault within the first year. The cost of repairing such a fault will be £125.

1. What is the probability that none of the machines will break down in the first year?
2. What is the probability that at least two machines will break down?
3. What is the probability that exactly three machines will break down?
4. How much money should be allocated over the next year to the repair budget for these machines?

Answer 27

Question 28

Now complement probabilities can be hard to understand, so if i say at least 3 what do i mean?

What is the probability of A^c ( complement)

Answer 28

1 - p(x<3)

1- p(x=0) + p(x=1) + p(x=3)

2) 1 - p(a)

Question 29

Question 3 (8 marks) ( first class for e and f)

A children’s book has 12 pages. The probability that any one page will have a typographical error (typo) is 0.15. Typos on different pages occur independently.

1. What is the probability of exactly four pages will have typo?
2. What is the average number of pages that have typo per book?
3. What is the probability that the number of pages with typo in a book will exceed the average?
4. What is the probability of at least one page has a typo?

A store has 8 such books. Typos occur independently in different pages and books.

1. What is the probability that at least two books have at least one page with typo?
2. What is the probability that only three books have no typos?

Answer 29