STATS AND PROB 1

• random experiment. is a process that can be repeated under similar conditions but whose outcome cannot be predicted with certainty beforehand.
• outcome is the result of a random experiment.
• A sample space is the collection of all possible outcomes of a random experiment.
• A sample point is an element of the sample space.
• event is a subset of the sample space whose probability is defined.
• Probability is a measure of the chances that an event may occur.Typically, the chances of a future outcome may be based on somepast experience of data collected.
• The population is the collection of all elements under consideration in astatistical inquiry.
• sample is a subset of population
• Descriptive Statistics includes all the techniques used inorganizing, summarizing, and presenting the data on hand.
• Nominal-level data - Data that can be only be categorized by labelling them
• Ordinal-level data - Data that can be categorized and ranked in an order but there is no equal interval between data points.
• Interval-level data - Data that can be categorized and ranked and exhibits equal intervals between neighboring data points. However, there is no true zero point.
• Ratio-level data - Data that can be categorized and ranked and infers equal intervals between neighboring data points. The data has a true zero point.
• Measures of Central Tendencv describe the center of a data set.
• Measures of Location describe the position of a certain data withrespect to the rest of the data set.
• Measures of Dispersion describe the variability or "scatteredness" ofa data set.
• The mean is calculated by adding up all the data values and dividing bythe number of data in the set (commonly known as the average).
• The median & is simply the middle value in a data set, arranged in anarray. The median is not affected by extreme values or outliers.
• The mode is the value that occurs most frequently. A data set can havemultiple modes.
• Measures of location describe the position of a certain data with respectto the rest of the data set.• Median: Minimum, maximum: Quartiles, deciles, and percentiles: Standard scores
• Measures of dispersion describes the variability or "scatteredness" of adata set.
• The range is the difference between the highest and lowest values inthe data set.
• The standard deviation is the average distances of each data pointfrom the mean.
• The variance is the average of squared distances of each data pointfrom the mean.
• Step1: represent the variable of interest

  ex: let h be the number of heads
• Step2: List down the sample space

  S = {HH, HT,TH, TT}
• Step3: assign numerical values to each outcomes
• Scratchwork: tree diagram
• 2 types of random variable: discrete (countable) , continuous (measurable)
• discrete random variable if its set takes a finite number of distinct values.
• continuous random variable if it assumes an infinite number of values in one or more intervals.
• A random variable is a function that associates a real number toeach outcome of an experiment. Capital letters are used torepresent a random variable.
• Discrete Probability Distribution another term: Probability mass function
• Discrete Probability Distribution. The probability distribution of a random variable designates probabilities to the possible values of a random variable.
• Step4: Construct the Frequency Distribution
• Step5: Construct the Probability Distribution
• The probabilities in a probability distribution are nonnegative. The minimum value is 0 and the maximum value should be 1.

  The sum of the probabilities for all the possible values of a random variable is equal to 1.
• The probability distribution of a discrete random variable can beshown graphically by constructing a histogram. The graph iscalled a probability histogram.
• mean also called expected value
• Step7: Compute the expected value