A die is weighted such that an even number is twice as likely to come out as an odd number. If the die is rolled and X is the number that turns up, construct the probability mass function for X and compute the expected value of X.
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- A die is weighted such that an even number is twice as likely to come out as an odd number. If the die is rolled and X is the number that turns up, construct the
probability massfunction for X and compute the expected value of X.
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Why use 9 for the denominator? why not 6 as there are 6 possible outcomes in tossing a die
how did you come up with the p(x). can you explain it further?
- Fill in the P(X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -4,0,1,2, and 4.A random variable X has the following probability mass function for x = 0, 1, 2, 5. Based (PMF): P(X= x) = (x+1) 12 on this PMF, what is P(X≥ 2)? 5/12 1/2 3/4 11/12Cards are picked sequentially without replacement from a well-shuffled deck of 52 cards until either all SPADES are found or all CLUBS are found. Let X denote the number of cards picked. Find E(X) using indicator random variables.
- The probability distribution function of the random variable Y is, y p(y) 0 0.287 1 0.456 2 0.001 3 0.256 Find Hy and Oy - Hy = 2.226,07 =1.123 Hly =1.226, o, = 1.578 a) b) Hy = 2.226,0; = 1.879 Hy =1.226, o; =1.123 c) d)eep st A spinner marked off in four equal-sized regions, numbered 8, 9, 10, and 11, is spun twice. Let the random variable X be the higher value resulting from th (or the common value if both spins have the same result.) Complete parts a through d. spi a) Write the probability mass function f(x) = P(X=x) as a set of ordered pairs. How is f(x)= P0X=x) calculated? O A. Divide the number of possible outcomes by the number of outcomes where X =x. O B. Divide the number of possible outcomes by the number of outcomes where X#x. O c. Divide the number of outcomes where X x by the number of possible outcomes. O D. Divide the number of outcomes where X=x by the number of possible outcomes. Choose the correct set of ordered pairs below. O A. ((三) O B. 10, C. 10, 16 O D. Cin ^n b) Find the cumulative probability function F, and draw its graph. Choose the correct cumulative probability function below. C. B. x<8 d x<8 1 x<8 16 8sx<9 16 asx<9 85x<9 16 F(x)= 9sx<10 F(x) = 95x<10 F(x) = < 5 9sx<10 16…Suppose we roll 3 fair dice and let X be the number of twos we roll.(a) Find the probability mass function of X.(b) Find the expected value of X.(c) Find the variance of X.(d) Find the probability-generating function of X.(e) Find the moment-generating function of X
- Let X denote a random variable having a distribution. If F(x)=ax³ where 0≤x≤(+3). Find f(x) after getting the constant value (a) and find the probability P(22. We have two fair dice, one red and one blue. When we roll them together, the outcome can be shown as an order pair, (R, B) where R and B are numbers from the red and the blue die, respectively. Let X be a random variable defined by X(R, B) = R - B where R and B are numbers from red and blue dice, respectively. (a) What is the probability mass function for the random variable? Show that as a table.A coin weighted so that P(H) = 2/3 and P(T) = 1/3 is tossed three times. Let X be the random variable which assigns to each point in the sample space the largest number of successive heads which occurs. Find the probability mass function of X.Fill in the P(X=x)values to give a legitimate probability distribution for the discrete random variable X, whose possible values are −2,1, 3, 4, and 5.The probability distribution function of a random variable X is 4. P(X =x)=Dk for x=0,1, 2,3,4 where k is a constant. Determine (a) the value of k. Hence, find P(0What value(s) of w will make this discrete probability model illegitimate? A. w > 0.1 B. w = 0.1 C. w < 0.1 D. Both A & C.Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman