Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Stats > Reading Quiz 8 > Flashcards

Reading Quiz 8 Flashcards

1
Q

binomial setting conditions

A
  1. each observation has two possible categories/outcomes, success or failure
  2. the observations are independent
  3. the probability of success, called p, is the same for each observation
  4. there is a fixed number of observations, n
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

binomial random variable

A

if data are produced in a binomial setting, then the random variable X = number of successes is called a binomial random variable

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

binomial distribution

A

if data are produced in a binomial setting, and the random variable X = number of successes is a binomial random variable, then the probability distribution of X is called a binomial distribution

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

binomial distribution

A

the distribution of the count X of successes in the binomial setting
parameters n and p

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

parameter n

A

number of observations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

parameter p

A

probability of a success on any one observation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

possible values of X

A

whole numbers from 0 to n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

X is

A

B(n,p)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

always be careful

A

to check when binomial distributions apply

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

binomial coefficient

A

number of ways of arranging k success among n observations given by this
(n choose k) = (n!)/(k!)(n-k)!

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

formula for binomial coefficients uses

A

factorial notation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

0!

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

(n choose k)

A

binomial coefficient n choose k

counts number of ways in which k successes can be distributed among n observations

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

binomial probability

A

if X has binomial distribution with n observations and probability p of success on each observation, the possible values of X are 0, 1, 2,…, n
if k is any one of these values:
P(X=k) = (n choose k) (p^k) (1-p)^(n-k) or
(n choose k) (p^k) (q)^(n-k)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

probability distribution function (pdf)

A

given a discrete random variable X
assigns a probability to each value of X
probabilities must satisfy the rules for probabilities given in chapter 6

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

cumulative distribution function (cdf)

A

given a random variable X
cdf of X calculates the sum of the probabilities for 0, 1, 2, up to the value X
calculates the probability of obtaining at most X successes in n trials

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

mean and standard deviation of a binomial random variable

A

if count X has binomial distribution with number of observations n and probability of success p,
mean = np
standard deviation = square root of ((np)(1-p)) or
square root of (npq)
BUT ONLY FOR BINOMIAL DISTRIBUTIONS CAN’T BE USED FOR OTHER DISCRETE RANDOM VARIABLES

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

normal approximation for binomial distributions

A

count X has binomial distribution with n trials and success probability p
when n is large, distribution of X is approximately normal, N(mean, standard deviation)
use normal approximation when n and p satisfy np greater than or equal to 10 and n(1-p) greater than or equal to 10 or nq greater than or equal to 10

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

geometric setting conditions

A
  1. each observation has two possible outcomes/categories, success or failure
  2. the observations are all independent
  3. the probability of a success, called p, is the same for each observation
  4. the variable of interest is the number of trials required to obtain the first success
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

how does geometric variable differ from binomial variable

A

in the geometric setting the number of trials varies and the desired number of defined successes (1) is fixed in advance

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

if X has geometric distribution with probability p of success and (1-p) failure on each observation

A

possible values of X are 1, 2, 3, etc. if n is any one of these values, the probability that the first success occurs on the nth trial is
P(X=n) = (1-p)^(n-1) (p) or
P(X=n) = q^(n-1) (p)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

mean and standard deviation of a geometric random variable

A

if X is geometric random variable with probability of success p on each trial,
mean/expected value = 1/p
variance = (1-p)/p^2 or
q/(p^2)
standard deviation is square root of variance formula

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

probability that it takes more than n trials to see first success is

A

P(X>n) = (1-p)^n or q^n

24
Q

Suppose someone looks at the numbers of 1’s, 2’s, 3’s, 4’s, 5’s, and 6’s that result from 600 die rolls. Is this situation an example of the “binomial setting”? Why or why not?

A

A. Almost, but not quite. For there to be a binomial setting, you have to have each observation fall into only two categories, rather than the 6 categories described here. However, if you defined a 1 as a “success” and anything else as a “failure,” then you would have a binomial setting, and you could then do the same thing separately with 2, 3, 4, 5, and 6.

25
Q

What are the four requirements for the binomial setting?

A

A. 1. Two categories: success or failure 2. Fixed # of observations 3. Independence 4. probability of
success same for all observations.

26
Q
  1. The distribution of the number of successes out of n trials (with probability of success p on each trial) is the ______ _______.
A

A. binomial distribution

27
Q

If someone has 51 socks in a drawer, with 1/3 red and 2/3 black, and the person grabs a handful of 5 of them, and counts the number of black, will the results of such a trial follow the binomial distribution? Why or why not?

A

A. Not quite, because grabbing a handful of 5 is equivalent to sampling without replacement. The probability of a black sock being included in the handful is altered some depending on what other socks are also in the handful. If you picked a sock one at a time, replaced the sock and mixed them thoroughly, and then picked again, the binomial distribution would apply.

28
Q

When we say a certain random variable has a B(100, 0.7) distribution, what do we mean?

A

A. That there is a binomial distribution with 100 observations and probability of success on each
observation is .7.

29
Q

If there is a discrete random variable (such as a binomial), and you want to find the probability of any given value of X, what function do you use – the cumulative distribution function or the probability distribution function? (cdf or pdf?)

A

pdf

30
Q

What are the formulas for the mean, variance, and standard deviation of a binomial random variable in terms of n and p, and, if you want, q (or 1-p).

A

A. mean:   np , variance:  2  npq and standard deviation:   npq

31
Q 
As a rule of thumb, the normal distribution may be used as an approximation to the binomial when both np
and nq (expected successes, expected failures) equal or exceed what number?
A

10

32
Q

For a binomial setting, the number of trials is fixed, and the random variable is the number of successes. For a geometric setting, the random variable is the number of ____ necessary to achieve the first ____.

A

trials, success

33
Q

What are the four requirements of the geometric setting?

A

A. 1. Two categories: “success” or “failure.” 2. Independent 3. Probability of success is the same for each observation. 4. Variable of interest is the number of trials required to obtain the first success.

34
Q
  1. In a geometric setting, with probability of success p, what is the probability that the first success will occur on the nth trial?
A

A. P(X  n)  1 pn1 por qn1 p

35
Q

True or False: the probabilities of success on the first, second, third, etc. trial in a geometric setting, when arranged in order, form a geometric series where p is the first term and each successive term being (1-p) (or q) times the previous one?

A

true

36
Q

True or False: if you apply the formula a/(1-r) for the sum of the terms of an infinite geometric series, where a is the first term and r is the ratio of each term to the previous one, for the geometric setting p is the first term and (1-p) is the ratio, so the sum becomes p/(1-(1-p)) or 1. Thus even though there are infinitely many possibilities for the outcome of the experiment in the geometric setting, the probabilities of each outcome sum to 1.

A

true

37
Q

If your chances of getting a success at anything in the geometric setting is p, what is the average or expected number of trials that you would have to conduct before getting a success?

A

1/p trials

38
Q
  1. If your chances of rolling a 1 on a die roll are one in 6, what is the expected or average number of times that you would have to roll the die before getting a 1?
A

6 times

39
Q

What is the variance in the geometric random variable?

A

A.1por q p2 p2

40
Q
  1. In the geometric setting, if q = 1 - p, what is the probability that it takes more than n trials to see the first success?
A

A. P(X  n)  (1 p)n or qn

41
Q

For a geometric distribution, would you say that it is approximately true that 34% of the observations would fall between the mean and 1 standard deviation above the mean, and 34% would fall between the mean and 1 standard deviation below the mean? Why or why not?

A

A. No, because the geometric distribution is always strongly skewed to the right, and its shape doesn’t resemble the normal distribution (for which the above statement is true).

42
Q

how to get on calc

A

2nd vars, binompdf/cdf/whatever, (# trials, probability, X=)

43
Q

equal sign

A

pdf

44
Q

inequality

A

cdf

45
Q

cdf counts

A

less than or equal to

46
Q

P(X=k)

A

binompdf(n, p, k)

47
Q

P(X less than or equal to k)

A

binomcdf(n, p, k)

48
Q

P(X less than k)

A

P(X less than or equal to k-1)

binomcdf(n, p, k-1)

49
Q

P(X greater than k)

A

1 - P(X less than or equal to k)

1 - binomcdf(n, p, k)

50
Q

P(X greater than or equal to k)

A

1 - P(X less than k)
1 - P( X less than or equal to k-1)
1 - binomcdf(n, p, k-1)

51
Q

rule check

A

np greater than or equal to 10

nq greater than or equal to 10

52
Q

geometric P(X=n)

A

2nd vars geometpdf(p, n)

53
Q

geometric P(X less than or equal to n)

A

2nd vars geometcdf(p, n)

54
Q

binomial mean and standard

A 
mean = np
standard = square root (npq)
55
Q

geometric mean and standard

A 
mean = 1/p
standard = square root (q/(p^2))

Stats (15 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions