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99問 • 1年前

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It is the branch of mathematics that deals with the likelihood or chance of different outcomes occurring in random experiment

Probability

It qualifies how likely an event to happen ranging from 0 to 1

Probability

It is a specific outcome or a set of outcomes from a random experiment

Event

The set of all possible outcomes of a random experiment

Sample space

The ratio of the number of favorable outcomes to the total number of possible outcomes

Probability of an event

What are the types of probability?

Theoretical probability, Experimental probability, Subjective probability

It is based on reasoning or calculations

Theoretical probability

It is based on actual experiments or historical data

Experimental probability

It is based on personal judgment or experience

Subjective probability

It is the sum of all the values in the set divided by the number of values

Mean

It is the middle value in a set when the values are arranged in ascending or descending order

Median

If the data set has an odd number of values, where does the median located?

The middle

If it has an even number of values, where does the median located?

It is the average of the two middle values

It is the value that appears most frequently in a data set

Mode

A data set can have more than one mode if multiple values have the same ______ Or it can have a no mode if all values are _______

Highest frequency, Unique

It is the set of all possible possible outcomes of random experiment. It provides comprehensive list of everything that can happen in that experiment.

Sample space

It can be defined as certain likely outcomes of an experiment that form a subset of a finite sample space

Events

Events in probability can be defined a certain likely outcomes of an experiment that form a subset of _____

finite sample space

It refers to all outcomes in the sample space that are not part of the event itself

complementary events

It includes all outcomes where some event does not occur

complement of an event

What are the key properties of complimentary events?

Mutually exclusive, Exhaustive, Sum of probabilities

It is an event where it’s complement, cannot occur at the same time

Mutually exclusive

It is an event where it’s complement, cover all possible outcomes in the sample space

Exhaustive

The probabilities of an event, and it’s compliment always add up to one

Some of probabilities

It refers to the event that both events occur simultaneously

Intersection events

These are events that cannot occur at the same time

Mutually exclusive events

If one event happens, the other cannot this event is called

disjoint events

From mutually exclusive event, probability of either event occurring in the sum of the individual probabilities

Addition rule

It refers to the event that at least one of events occurs

Union events

It helps us find the probability of two events happening together

Multiplication rule

There are two versions of multiplication rule

Independent, Dependent event

It is the probability that both events occurring is the product of their individual probabilities

Independent events

It is where the probability of both events occurring as the product of the probability of the first event, and the conditional probability of the second event, given that the first event has occurred

Dependent event

It refers to an arrangement of objects in specific order

Permutation

It is the arrangement of items in a circle and starting point is not fixed

Circular permit

This is where the formula adjust to account for the repeated items

Circular permutation

It is used to determine the number of ways to choose a subset of items for larger set where the order of the selection does not matter

Combination rule

It is often used in probability to calculate the number of ways to arrange or select objects

factorial rule

It is the product of our positive integers

Factorial of a number

It’s states that the sum of probability of an event, and the probability of its compliment is always equal to one

Complimentary rule

It is the probability of an event occurring given that another event has already occurred

Conditional probability

What is the significance of conditional probability?

It helps us understand how the occurrence of one event affects the likelihood of another event

It is the probability theory that describes how to update the probability of a Hypothesis base on any new evidence

Baye’s Rule

represents in numerical value associated with each outcome of a probability distribution

Random variables

A random variable is discreet if it has _______ Possible outcomes that can be listed

Finite or countable number log

A random variable is continuous if it has _______ Represented by the intervals on a number line

Uncountable number or possible outcomes

It is equal to the mean of random variable

Expected value

At least each possible value, the random variable can assume together with its probability

Discrete, probability distribution

What are the two conditions of discrete probability distribution?

The probability of each value of the discrete, random variable is between zero and one inclusive, The sum of all the probabilities is one

It is denoted by the FFX measures the probability, the random variable X assume a value less than or equal to one

Cumulative distribution function

It is the adding app of the probabilities up to a certain value

Cumulative probability

What are the following condition that satisfies the binomial experiments?

Experiment is repeated for a fixed number of trials, where trials is independent of the other trials, There are only two possible outcomes of interest for each trial. The outcomes can be classified as success, or as a failure., The probability of success is the same for each trial, The random variable X count the number of successful trials

It has a probability, assuming exactly any of its values

Continuous, random variable

It has number of values they can assume is non-countable

Continuous, random variable

There are an ______ Possibilities that the land could be so the probability could be zero

Infinite number

It is a function that describes how likely particular outcomes or intervals deals with the continuous random variables

Probability density function

It is the probability that the random variable X is between values

The area under the PDF in a specific region

If you take all the probabilities that are variable could be, then they’re probabilities must

add up to one

The normal density function was proposed by

C.F Gauss (1777-1855)

It is defined as second continuous frequency, distribution of infinite range

Normal distribution

It is a descriptive model that describes the real world situations

Normal distribution

These are lines that shows the location of the individuals along the horizontal axis, and within the range of possible values

Density curve

Describes the overall pattern of a distribution the area under the curve, and above any range of values on the horizontal axis is the proportion of all observations that fall in that range

Density curves

The overall pattern of a distribution under the area under the curve, and above any range of values and horizontal axis, is the _______ Of all observations that fall in that range

Proportion

It is the balance point in a density curve

Mean

It is an equal areas point or the point that divide the under the curve in half

Median

The mean, and the median are the same for _________

Symmetric density curve

They both lie at the center of the curve

Mean and median

It is described by a normal density curve

Normal distribution

It is any particular normal distribution is completely specified by two numbers

Mean and standard deviation

Where is the distance from the center to the change of curvature points on either side

Standard deviation

Normal distribution are symmetric around _____

Mean

The main median and mode of a normal distribution are ______

Equal

Normal distribution are ________ In the center and _______ in the tails

denser, less dense

How many percentage of the area of of a normal normal distributions are within one standard deviation of the mean?

68%

Approximately what percentage of the area of a normal distribution is within two standard deviation of the mean

95%

It is a value from any normal distribution that can be transformed into its corresponding value

Standard normal distribution

In standard normal distribution Z is what

Value standard normal distribution

A standard normal distribution X is what

The value on the original distribution

Grouping or subset of items

Combination formula

It is the measure of dispersion, or scatter in the possible value for X in a random variable

Variance

It uses weight as the multiplier of each possible square deviation

Variance

Is a weighted Average average of the possible values of X with weights equal to the probabilities

Mean

FFFX is the probability mass function of loading on long, thin beam. It is the point at the beam balances.

Mean

It describes the center of distribution of X in a manner similar to the balance point of loading

Mean

If the semester of the center or middle of the probability distribution

Mean

It is the measure of a dispersion or variability in the distribution

Variance

It is a description of the probabilities associated with the possible values of X

Probability distribution

Specified by just a list of the possible values, along with the probability of each

Discrete, random variable

It is denoted by an uppercase letter, such as X

Random variable

It is a function that a science are real number to each outcome in the ample space of veranda experiment

Random variable

It’s used to distinguish between a random variable, and the real number

Notation

It is the variable that associates a number with the outcome or experiment

Random variable

It is a random variable with an interval of real numbers for its range

Continuous, random variable

Can be used to describe the probability distribution of a continuous, random variable

Probability density function

Provides a simple description of the probabilities associated with a random variable

Probability density function

It is an approximation to probability density function

Histogram

The distribution is often specified by just a list of the possible values, along with the probability of each

Discrete, random variable

It is the distance from the center to the change of curvature points on either side

Standard deviation

Materials

ユーザ名非公開 · 100問 · 1年前

Materials