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wnioskowanie statystyczne Lernen beginnen
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the branch of statistics which is concerned with using probability concept to deal with uncertainly in decision making. It refers to the process of selecting and using a sample to draw inference about population from which sample is drawn.
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statystyka opisowa Lernen beginnen
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its aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
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wnioskowanie statystyczne Lernen beginnen
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the branch of statistics which is concerned with using probability concept to deal with uncertainly in decision making. It refers to the process of selecting and using a sample to draw inference about population from which sample is drawn.
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ELEMENTS OF STATISTICAL INFERENCE Lernen beginnen
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Estimation of population value (point estimation or range estimation), testing of hypothesis
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a complete set of elements being studied defined in terms of material (who or what is the subject of the study), spatial (where the community is located) and time (what moment or period the study concerns)
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(research unit, observation unit) Lernen beginnen
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components of the community being studied
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an object that provides information about the properties of statistical units e.g. the reporting unit is a person who conducts an interview for the purposes of the General Agricultural Census (in this case, the statistical unit is a farm)
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zmienna Lernen beginnen
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characteristics or attribute of a statistical unit, which can be assume different values for different units
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A random variable is a variable Lernen beginnen
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A random variable is a variable whose value is determined by a random experiment.
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discrete (having specific values) continuous (any value in a continuous range).
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discrete variable is a variable whose value is obtained by counting number of students present, number of red marbles in a jar, number of heads when flipping three coins, students’ grade level
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is a variable whose value is obtained by measuring height of students in class, weight of students in class, time it takes to get to school, distance traveled between classes
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is an outcome result or defined collection of outcomes of a random experiment. Since the collection of all possible outcomes to a random experiment is called the sample space, another definiton of event is any subset of a sample space.
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An event connected with the theory of probability may be any of the following types: Lernen beginnen
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(1) Sure event, (2) Impossible event, (3) Random event 4 ) Simple event, 5 ) Compound event combination of simple events
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these are two events from one family of events (event space), the sum of which is a certain event (A υ B = Ω) and the intersection is an empty set (A B = ∅∅) i.e. the product of each two different events is an empty set. The opposite events form a complete system of events. The event opposite to A is marked as A ', similarly, the event opposite to A' is event A.
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The probability of an event Lernen beginnen
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probability of an event is the number of favorable outcomes divided by the total number of outcomes The probability of an event tells us how likely that event is to occur. We usually write probabilities as fractions or decimals.
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P(E) comes from an experiment 𝑃(𝐸)= #𝑠𝑢𝑐𝑐𝑒𝑠𝑠 / #𝑡𝑟𝑖𝑎𝑙𝑠
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P(E) comes from a „ thought ” experiment 𝑃(𝐸) =#𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑠𝑢𝑐𝑐𝑒𝑠𝑠 / #𝑝𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠
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The ski club is holding a raffle to raise money. They sold 100 tickets. All of the tickets are placed in a jar. Find the probability of winning the prize for each person. One ticket will be pulled out of the jar at random, and the winner will receive a prize. Ann bought one raffle ticket. Jane bought 2 tickets and Joe 20. Lernen beginnen
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Ann 1/100=0.01 Jane 2/100=0.02 Joe 20/100=0.2
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𝑇ℎ𝑒 𝑝𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 𝑜𝑓𝑒𝑎𝑐ℎ 𝑒𝑣𝑒𝑛𝑡 Lernen beginnen
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𝑖𝑠 𝑎 𝑛𝑢𝑚𝑏𝑒𝑟 𝑖𝑛 𝑡ℎ𝑒 𝑟𝑎𝑛𝑔𝑒 [0;1:]
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The probability of an impossible event Lernen beginnen
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The probability of an event A 'that is opposite to event A is Lernen beginnen
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is equal to: P(A’)=1-P(A)
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If random event A is included in random event B (𝐴⊂𝐵), Lernen beginnen
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The probability of the sum of any two random events A and B is Lernen beginnen
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equal to the sum of the probabilities of these events minus the probability of their product:
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The sum of the probabilities of all events is Lernen beginnen
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When calculating empirical probability the more repetitions the experiment, the closer the empirical probability is to the „ acual ” probability
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Poisson distribution is a probability distribution that is used to show how many times an event is likely to occur over a specified period. In other words, it is a count distribution. Poisson distributions are often used to understand independent events that occur at a constant rate within a given interval of time.
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a normal distribution is a type of continuous probability distribution for a realvalue random variable A variable that is normally distributed has a histogram (or density function) that is bell shaped, with only one peak, and is symmetric around the mean. In a normal distribution, the mean, median, and mode are equal.
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what is the most commonly used distribution in statistics. Lernen beginnen
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RANDOM VS. STANDARISED VARIABLE Lernen beginnen
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By standardizing a random variable X, we obtain a standardized variable Z (0,1)
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