Random Variable Reviewer Set PDF

LESSON 1.1: RANDOM VARIABLE REVIEWER SET. - Who is the Father of Modern Statistics and Experiment Design? [Sir. Ronald Aylmer Fisher.] - [Random Experiment] an experiment that repeated numerous times under the same condition or the result must be independent to one another. - [O...

LESSON 1.1: RANDOM VARIABLE REVIEWER SET. - Who is the Father of Modern Statistics and Experiment Design? [Sir. Ronald Aylmer Fisher.] - [Random Experiment] an experiment that repeated numerous times under the same condition or the result must be independent to one another. - [Outcome] is the result of a random experiment or usually known as "consequence" ? - [Random Variable] is a function that associates a numerical value to every outcome of a random experiment; denoted by a capital letter, usually X. - [Sample Space] is the setof possible outcomes of a random experiment; denoted by a capital letter, usually S. - The [Domain] is the sample space, and the [Range] is some set real numbers. - The domain is usually called [Independent variable] or capital X. - What is the range of a random variable?[Some set of real numbers.] - Which is **NOT** a random variable? [The number of babies born in the Philippines in 2015] - An experiment involves tossing three fair coins. How many elements are there in the domain? **Explaination:** Let H and T represent coin tosses that result in heads and tails, respectively. The domain or the sample space of tossing three coins is {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT} Thus, there are [eight elements] in the domain. - An experiment involves tossing five coins. How many elements are there in the domain? Without listing, the number of elements in the domain of tossing coins can be determined using the formula 2  where   is the number of tosses. Therefore, there are [32 elements] in its domain - ***Situation:*** A human resource manager is researching about the trend of employee hiring on several startup companies who are looking to expand operations. The table below shows the projected number of employees to be added. What is the random variable involved in the study? [Target hires]. - ***Situation:*** Two dice are rolled. If X is the sum of the identical numbers on the two dice, then what is the range of X? [{2, 4, 6, 8, 10, 12}] **Explanation:** The range of X is the set containing the 6 values of X. - ***Situation:*** Suppose that you toss three fair coins. You get a score of 1 for each coin that shows tails and  -1 for each coin that shows heads. Let X be your total score. What values can the random variable X take? --3, --1, 1, and 3 **Explanation:** The sample space will be\ S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}. Based on the rule, a score of 1 is obtained for every tail and --1 for every head. For example, the outcome THT corresponds to a score of 1+(--1)+1=1. These are the corresponding values of X based on the rule: X = {--3,--1,--1,1,--1,1,1,3} Thus, the random variable X can assume the values --3, --1, 1, and 3. - What is the domain when two coins are tossed? **Explanation:** The domain is the sample space. Thus, [S = {HH, HT, TH, TT}] - ***Situation:***A mother will give birth to a twin. If X denotes the number of boys, what are the possible values of X? 0, 1, and 2. What is the sample space model of getting a chance twin boys? [𝑆 = {GG, BG, BB}] - A die is rolled twice. Let Y be a random variable that denotes the number of even numbers that appear. What are the possible values of Y? [0, 1, and 2.] - ***Situation:*** A technician must choose three chips at random from four chips, two of which are defective. Let Z represent the number of non-defective chips chosen. What are the possible values of Z given that the first chip chosen is defective? [1 and 2.] **Explanation:** It is given that the first chip chosen is defective. Thus, we have the following tree diagram.  What is the sample space model of getting a chances to get a number of non-defective chips? [ 𝑆 = {DDF, DFD, DFF}] - What is the proper model of sample space of the blue marbles? [𝑆 = {RR, RB}] Is this the proper mapping chart of possible outcome of blue marbles? [Yes] This Is from your [QUIPPER BASED EXAMPLES] - ***Situation:*** A researcher is conducting a study about the number of shows which fifty regular employees watch at night before they rest. If X is a random variable that denotes the number of shows they watch every night before they rest, what are the possible values of X? [1, 2, 3,..., 50.] - ***Situation:*** There are 10 students in a cafeteria. If X denotes the number of males, what are the possible values of X? [X = 0, 1, 2,... ,10] - ***Situation:*** A cinema can accommodate 200 customers. Let Z denote the number of customers in the cinema. What are the possible values of Z ? [Z = 0, 1, 2,... , 200] - ***Situation:*** A researcher is conducting a survey about the cellphones used by 50 employees. If X represents the number of users of Brand X, what are the possible values of X? [X = 0, 1, 2,... , 50] - ***Situation:*** A bus can accommodate a maximum of 60 passengers. If X denotes the number of male passengers, what are the possible values of X? [X = 0, 1, 2,... , 60] - ***Situation:*** Two coins are tossed simultaneously. The outcome of the first coin is head. Let X be a random variable that denotes the number of heads that appear. What are the possible values of X? [X = 1, 2] - ***Situation:*** A jeepney can accommodate 16 passengers. If X denotes the number of male passengers in the jeepney when it is full, what are the possible values of X? [X = 0, 1, 2,... , 16 ]