Brainscape's Knowledge GenomeTM

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


See full index

Stats 2019 > Probability Distributions > Flashcards

Probability Distributions Flashcards

1
Q

What shape does a graph of a normal distribution have

A

a “bell shape”

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

what are the parameters of the normal distribution

A

the mean and standard deviation

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

in a normal distribution, approximately ____ of the values lie between one standard deviation below the mean and one standard deviation above the mean

A

68%

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

in a normal distribution, approximately ____ of the values lie between two standard deviations below the mean and two standard deviations above the mean

A

95%

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

in a normal distribution, approximately ____ of the values lie between three standard deviations below the mean and three standard deviations above the mean

A

99%

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

The total area under a normal distribution curve is?

A

1

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

when is a continuity correction required

A

when normal distributions are used to approximate situations that are actually discrete, for example, when measurements are rounded

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

how do you do a continuity correction

A

for example, if something is measured to the nearest centimetre, it could be half a centimetre below the value in order to be counted as that value, so you put the value half a centimetre below the value into your calculator to get your answer

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

what is an inverse normal distribution

A

when we are given a probability and need to work backwards to find an x value (or the mean or standard deviation)

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

is a triangular distribution continuous or discrete

A

continuous

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

what are the parameters of the triangular distribution

A 
a = minimum 
b = maximum
c = mode (most likely value or peak)
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

in a triangular distribution, which feature of the graph shows the probability

A

area under the function (triangle)

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

what is the height of the peak of a triangular distribution

A

2/b-a

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

which part of the formula do you use to find the height of a point on the triangle on the left side

A

top one

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

which part of the formula do you use to find the height of a point on the triangle on the right side

A

bottom one

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

what is the formula for the area of a triangle

A

0.5 x base x height

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

is the uniform distribution continuous or discrete

A

continuous

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

what shape is the uniform distribution

A

rectangle

19
Q

in what situations is the uniform model used

A

where outcomes are expected to occur within a particular range of values and each value within the range is equally likely to occur

20
Q

what are the parameters of the uniform distribution

A 
a = minimum
b = maximum
21
Q

what feature of the uniform distribution shows the probability

A

area under the function

22
Q

what formula can be used to find the height of the rectangle for the uniform distribution

A

1/b-a

23
Q

what is the approach we use for an inverse question for both triangular and uniform distributions

A

to form and solve an algebraic expression by setting the area formula equal to the known probability

24
Q

for an inverse triangular distribution question, what form do you want to get the algebraic expression into?

A

a quadratic equation on the top of the fraction for the height, make this a quadratic equation equal to 0, then you will be able to use your calculator to solve it and discard a value that isn’t possible

25
Q

what are the models for continuous distributions

A

normal, triangle, uniform

26
Q

what do we call just a regular ‘discrete’ distribution

A

the table thingy with values for x and the probabilities for these

27
Q

how do you work out a mean E(x) of a regular ‘discrete’ distribution

A

multiply and add

multiply the x value by the probability of everything in the table and add them all together

28
Q

how do you find the variance of a regular ‘discrete’ distribution

A

square the x values, then multiply these by the original probabilities and add these all together

then minus the mean squared to get the variance

29
Q

how do you get the standard deviation of a regular ‘discrete’ distribution

A

square root of the variance

30
Q

expected value is also known as?

A

the mean

31
Q

the notation for expected value is?

A

E[x]

32
Q

what is the notation for variance

A

Var[x]

33
Q

true or false, VAR[X-Y] = VAR[X]+VAR[Y]

A

true, always add variances

34
Q

when is the binomial distribution used

A

when calculating the probability of a certain number of ‘successes’ out of a fixed number of trials

35
Q

what are the conditions of the binomial distribution

A
  1. the number of trials must be fixed
  2. there are only two possible outcomes for each trial (‘success’ and ‘failure’)
  3. the probability of success at each trial must be the same
  4. each trial must be independent of the others
36
Q

what are the parameters of the binomial distribution

A

n (numtrial) represents the number of trials conduted

p is the probability of success for each trial

37
Q

how do you primarily solve binomial and poisson problems

A

in your calculator: stat dist binm or poiss ppd or pcd or bcd or bpd.

38
Q

is binomial discrete or continuous

A

discrete

39
Q

is poisson discrete and continuous

A

discrete

40
Q

when do you use a poisson distribution

A

represents the number of times an event occurs in a specific length of time or amount of space

41
Q

what are the conditions of the poisson distribution

A
  1. events cannot occur simultaneously
  2. each occurrence is independent of the other occurrences
  3. events occur at random, and are unpredictable
  4. for a small interval, the probability of the event occurring is proportional to the size of the interval
42
Q

what is the parameters of the poisson distribution

A

λ - the mean number of times the event occurs in a particular interval

43
Q

in a graph of a discrete distribution, what feature represents the probabilities of each value

A

the heights of the bars

Stats 2019 (2 decks)

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