Determine whether or not the table is a valid probability distribution of a discrete random variable. This site is using cookies under cookie policy . If the ball lands in an even numbered slot, he receives back the dollar he bet plus an additional dollar. Continuous If so, give the values of \(n\) and\(p\). Let \(X\) denote the net gain from the purchase of a randomly selected ticket. The prizes and chances of winning are listed in the offer as: \(\$5\) million, one chance in \(65\) million; \(\$150,000\), one chance in \(6.5\) million; \(\$5,000\), one chance in \(650,000\); and \(\$1,000\), one chance in \(65,000\). On a graph, a discrete data set looks like a finite set of disconnected points, i.e.. On a graph, a continuous data set looks like a smooth line or curve, i.e.. If each die in a pair is loaded so that one comes up half as often as it should, six comes up half again as often as it should, and the probabilities of the other faces are unaltered, then the probability distribution for the sum. When dropped on a hard surface a thumbtack lands with its sharp point touching the surface with probability \(2/3\); it lands with its sharp point directed up into the air with probability \(1/3\). standard deviation, = 8 An insurance company will sell a \(\$10,000\) one-year term life insurance policy to an individual in a particular risk group for a premium of \(\$368\). Instead of testing all \(600\) blood samples to find the expected \(12\) diseased individuals, investigators group the samples into \(60\) groups of \(10\) each, mix a little of the blood from each of the \(10\) samples in each group, and test each of the \(60\) mixtures. The length of time to play 18 holes of golf (Y) is a continuous variable, as it can take 2 hours, or 2.5 hours, or 2 hours, 30 minutes, 2 seconds, one measures how long it took to play 18 holes to know Y. It is seen as a part of artificial intelligence.. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly . You can specify conditions of storing and accessing cookies in your browser, B Classify the following random variables as discrete or continuous, 1. the number of defective computers produced by a manufacturer. Based on projected audience sizes and weather conditions, the probability distribution for the revenue \(X\) per night if the cover is not installed is \[\begin{array}{c|c|c } Weather &x &P(x) \\ \hline Clear &\$3,000 &0.61 \\ Threatening &\$2,800 &0.17 \\ Light Rain &\$1,975 &0.11 \\ Show-cancelling\; rain &\$0 &0.11 \\ \end{array}\]The additional cost of the cover is $410,000. Each month a local blood bank sends an appeal to give blood to \(250\) randomly selected students. span(X). So, it is a continuous variable. as described in the main body of the text. 46. what pairs of lines are parallel? C.i=95% b) Find the equation of the, A:Dependent variable (y) = Final grade of the student The time needed to finish the test 4. 13. Let X be a discrete random variable with the following PMF. .. Grapefruit are sold by the dozen. Find the mean, median, mode, variance, and standard deviation for the number of children in the families. the length of time to play 18 holes of golf. c.M: the amount of milk produced yearly by a particular cow. A laboratory performs \(20\) such tests daily. The amount of liquid in a \(12\)-ounce can of soft drink. A discrete random variable \(X\) has the following probability distribution: \[\begin{array}{c|c c c c c} x &77 &78 &79 &80 &81 \\ \hline P(x) &0.15 &0.15 &0.20 &0.40 &0.10 \\ \end{array}\]Compute each of the following quantities. Variable M consists of amount of milk produced which can't be counted but can be measured. Discrete Continuous Continuous Continuous The weight of a box of cereal labeled \(18\) ounces.. The weight of the professional wrestler. ff- if its set of possible outcomes is countable. Discrete 2) Amount of milk used per drink. Book: Introductory Statistics (Shafer and Zhang), { "4.01:_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.02:_Probability_Distributions_for_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.03:_The_Binomial_Distribution" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "4.E:_Discrete_Random_Variables_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Introduction_to_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Descriptive_Statistics" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Basic_Concepts_of_Probability" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Discrete_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Continuous_Random_Variables" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Sampling_Distributions" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Estimation" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Testing_Hypotheses" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Two-Sample_Problems" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Correlation_and_Regression" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_Chi-Square_Tests_and_F-Tests" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 4.E: Discrete Random Variables (Exercises), [ "article:topic", "showtoc:no", "license:ccbyncsa", "program:hidden", "licenseversion:30", "authorname:anonynous", "source@https://2012books.lardbucket.org/books/beginning-statistics" ], https://stats.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fstats.libretexts.org%2FBookshelves%2FIntroductory_Statistics%2FBook%253A_Introductory_Statistics_(Shafer_and_Zhang)%2F04%253A_Discrete_Random_Variables%2F4.E%253A_Discrete_Random_Variables_(Exercises), \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\). The probability that an egg in a retail package is cracked or broken is \(0.025\). Suppose the number \(00\) is considered not to be even, but the number \(0\) is still even. Find the expected value to the company of a single policy if a person in this risk group has a \(97.25\%\) chance of surviving one year. "Introductory Statistics" by Shafer and Zhang. Interpret the mean in the context of the problem. Will the owner have the cover installed? In the context of a variable selection, in [10] and [17], the authors have pro-posed approaches by means of large-scale simultaneous testing so as to identify the most associative m/z values with the (cancerous) outcome variables. 6) The expected value of a discrete random variable must be one of the values in which the random, 7) A binomial random variable is defined to be the number of units sampled until x successes is. \(X\) is the number of hearts in a five-card hand drawn (without replacement) from a well-shuffled ordinary deck. Shylock enters a local branch bank at \(4:30\; p.m\). Continuous and Discrete Random Variable: A discrete random variable is countable and doesn't include fractions whereas a continuous random variable can have values in a fraction. Classify the following random variables as discrete or continuous. Q: the weight of grain produced per acre. Represent Measured data. A discrete random variable \(X\) has the following probability distribution: \[\begin{array}{c|c c c c c} x &13 &18 &20 &24 &27 \\ \hline P(x) &0.22 &0.25 &0.20 &0.17 &0.16 \\ \end{array}\]Compute each of the following quantities. A box that contains two or more grapefruit of inferior quality will cause a strong adverse customer reaction. Classify each random variable as either discrete or continuous. The pattern evident from parts (a) and (b) is that if. Q:What is the standard deviation of this distribution? Louki Akrita, 23, Bellapais Court, Flat/Office 46, 1100, Nicosia, Cyprus. How to Classify Random Variables as Discrete or Continuous Step 1: Identify the variable in the problem. Pizza The weight of the professional wrestlers 6. Thus, this variable can be measured to any fraction of a second. If either one of the units is defective the shipment is rejected. Find the probability that at least one of them will be able to speak English. The number of breakdowns of city buses in a large city in one week. \ ( \mathrm {W}= \) the total surface area of a randomly selected person's body \ ( X= \) the quantity of oil in a randomly selected oil spill in the sea \ ( \mathrm {Y}= \) the quantity of pots in a randomly selected restaurant kitchen \ ( Z \) = the total cent value of types of variables in statistics ppter wait times university hospital. Let \(X\) denote the number of boys in a randomly selected three-child family. Suppose a shipment has \(5\) defective units. The speed of the car 2. 26/02/2023 . The number of accident-free days in one month at a factory. 4.8 (9 reviews) Term 1 / 10 the number of defective computers produced by a manufacturer Click the card to flip Definition 1 / 10 discrete Click the card to flip Flashcards Learn Test Match Created by quizlette7862173 Terms in this set (10) First, we have to know the difference between discrete and continuous variables: This site is using cookies under cookie policy . Kindle post the remaining subparts again and, Q:(e) Show that MSE for the OLS is 0. Classify the following random variable according to whether it is discrete or continuous. Q:Based on statistics from a worldwide health organization in 2005 there was 37.4 Million people. Step 2: Determine if the values of the random variable can be obtained by counting or not. D = domestic flight. Variable N consists of number of eggs laid which can be counted. This page titled 4.E: Discrete Random Variables (Exercises) is shared under a CC BY-NC-SA 3.0 license and was authored, remixed, and/or curated by via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. For this study, we should use [Select an answer The denominator isn't zero. The probability that he will, Q:Calculate r, the correlation coefficient ________________ the number of defective computers produced by a manufacturer. Classify the following random variables as discrete or continuous: a.X: the number of automobile accidents per year in Virginia. As sometimes happens with probabilities computed as empirical relative frequencies, probabilities in the table add up only to a value other than \(1.00\) because of round-off error. Circle the correct answer. Step 2: Determine if the values of the random variable can be obtained by. Are the number of leaves on a tree a discrete or continuous variable? It is important to note that this variable was not specified to an hour, a minute, etc. The amount of sugar in a cup of coffee 6. 2. Ten percent of all purchasers of a refrigerator buy an extended warranty. The time, to the nearest whole minute, that a city bus takes to go from one end of its route to the other has the probability distribution shown. Discrete Moment generating function of X is 1) Classify the following random variable according to whether it is discrete or continuous. A fair coin is tossed repeatedly until either it lands heads or a total of five tosses have been made, whichever comes first.
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