問題一覧
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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
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It qualifies how likely an event to happen ranging from 0 to 1
Probability
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It is a specific outcome or a set of outcomes from a random experiment
Event
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The set of all possible outcomes of a random experiment
Sample space
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The ratio of the number of favorable outcomes to the total number of possible outcomes
Probability of an event
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What are the types of probability?
Theoretical probability, Experimental probability, Subjective probability
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It is based on reasoning or calculations
Theoretical probability
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It is based on actual experiments or historical data
Experimental probability
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It is based on personal judgment or experience
Subjective probability
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It is the sum of all the values in the set divided by the number of values
Mean
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It is the middle value in a set when the values are arranged in ascending or descending order
Median
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If the data set has an odd number of values, where does the median located?
The middle
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If it has an even number of values, where does the median located?
It is the average of the two middle values
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It is the value that appears most frequently in a data set
Mode
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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
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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
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It can be defined as certain likely outcomes of an experiment that form a subset of a finite sample space
Events
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Events in probability can be defined a certain likely outcomes of an experiment that form a subset of _____
finite sample space
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It refers to all outcomes in the sample space that are not part of the event itself
complementary events
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It includes all outcomes where some event does not occur
complement of an event
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What are the key properties of complimentary events?
Mutually exclusive, Exhaustive, Sum of probabilities
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It is an event where it’s complement, cannot occur at the same time
Mutually exclusive
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It is an event where it’s complement, cover all possible outcomes in the sample space
Exhaustive
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The probabilities of an event, and it’s compliment always add up to one
Some of probabilities
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It refers to the event that both events occur simultaneously
Intersection events
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These are events that cannot occur at the same time
Mutually exclusive events
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If one event happens, the other cannot this event is called
disjoint events
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From mutually exclusive event, probability of either event occurring in the sum of the individual probabilities
Addition rule
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It refers to the event that at least one of events occurs
Union events
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It helps us find the probability of two events happening together
Multiplication rule
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There are two versions of multiplication rule
Independent, Dependent event
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It is the probability that both events occurring is the product of their individual probabilities
Independent events
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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
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It refers to an arrangement of objects in specific order
Permutation
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It is the arrangement of items in a circle and starting point is not fixed
Circular permit
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This is where the formula adjust to account for the repeated items
Circular permutation
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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
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It is often used in probability to calculate the number of ways to arrange or select objects
factorial rule
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It is the product of our positive integers
Factorial of a number
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It’s states that the sum of probability of an event, and the probability of its compliment is always equal to one
Complimentary rule
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It is the probability of an event occurring given that another event has already occurred
Conditional probability
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What is the significance of conditional probability?
It helps us understand how the occurrence of one event affects the likelihood of another event
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It is the probability theory that describes how to update the probability of a Hypothesis base on any new evidence
Baye’s Rule
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represents in numerical value associated with each outcome of a probability distribution
Random variables
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A random variable is discreet if it has _______ Possible outcomes that can be listed
Finite or countable number log
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A random variable is continuous if it has _______ Represented by the intervals on a number line
Uncountable number or possible outcomes
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It is equal to the mean of random variable
Expected value
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At least each possible value, the random variable can assume together with its probability
Discrete, probability distribution
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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
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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
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It is the adding app of the probabilities up to a certain value
Cumulative probability
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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
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It has a probability, assuming exactly any of its values
Continuous, random variable
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It has number of values they can assume is non-countable
Continuous, random variable
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There are an ______ Possibilities that the land could be so the probability could be zero
Infinite number
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It is a function that describes how likely particular outcomes or intervals deals with the continuous random variables
Probability density function
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It is the probability that the random variable X is between values
The area under the PDF in a specific region
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If you take all the probabilities that are variable could be, then they’re probabilities must
add up to one
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The normal density function was proposed by
C.F Gauss (1777-1855)
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It is defined as second continuous frequency, distribution of infinite range
Normal distribution
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It is a descriptive model that describes the real world situations
Normal distribution
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These are lines that shows the location of the individuals along the horizontal axis, and within the range of possible values
Density curve
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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
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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
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It is the balance point in a density curve
Mean
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It is an equal areas point or the point that divide the under the curve in half
Median
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The mean, and the median are the same for _________
Symmetric density curve
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They both lie at the center of the curve
Mean and median
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It is described by a normal density curve
Normal distribution
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It is any particular normal distribution is completely specified by two numbers
Mean and standard deviation
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Where is the distance from the center to the change of curvature points on either side
Standard deviation
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Normal distribution are symmetric around _____
Mean
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The main median and mode of a normal distribution are ______
Equal
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Normal distribution are ________ In the center and _______ in the tails
denser , less dense
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How many percentage of the area of of a normal normal distributions are within one standard deviation of the mean?
68%
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Approximately what percentage of the area of a normal distribution is within two standard deviation of the mean
95%
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It is a value from any normal distribution that can be transformed into its corresponding value
Standard normal distribution
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In standard normal distribution Z is what
Value standard normal distribution
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A standard normal distribution X is what
The value on the original distribution
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Grouping or subset of items
Combination formula
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It is the measure of dispersion, or scatter in the possible value for X in a random variable
Variance
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It uses weight as the multiplier of each possible square deviation
Variance
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Is a weighted Average average of the possible values of X with weights equal to the probabilities
Mean
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FFFX is the probability mass function of loading on long, thin beam. It is the point at the beam balances.
Mean
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It describes the center of distribution of X in a manner similar to the balance point of loading
Mean
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If the semester of the center or middle of the probability distribution
Mean
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It is the measure of a dispersion or variability in the distribution
Variance
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It is a description of the probabilities associated with the possible values of X
Probability distribution
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Specified by just a list of the possible values, along with the probability of each
Discrete, random variable
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It is denoted by an uppercase letter, such as X
Random variable
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It is a function that a science are real number to each outcome in the ample space of veranda experiment
Random variable
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It’s used to distinguish between a random variable, and the real number
Notation
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It is the variable that associates a number with the outcome or experiment
Random variable
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It is a random variable with an interval of real numbers for its range
Continuous, random variable
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Can be used to describe the probability distribution of a continuous, random variable
Probability density function
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Provides a simple description of the probabilities associated with a random variable
Probability density function
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It is an approximation to probability density function
Histogram
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The distribution is often specified by just a list of the possible values, along with the probability of each
Discrete, random variable
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It is the distance from the center to the change of curvature points on either side
Standard deviation