QUESTION 3 - problem-type question requiring detailed written answers. (a) Table 3 below shows all the possible values of a discrete random variable, X, and their corresponding probabilities. X P(X=X) -3 0.14 -1 0 1 0.22 0.36 0.20 0.08 3 (i) Find P(-3 ≤X < 0), P(X≥0) and P(X<3) (ii) Calculate the expected value (mean) and the standard deviation of the probability distribution.
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- Solve the below problem. Table 1 contains the probabilities associated with each possible pair of values for Y, and Y, and is known as the joint probability function for Y,and Y2 Table: Probability function for Y, and Y, Yı_ y2 0 1 2 0 1/9 2/9 1/9 2/9 2/9 0 1 | 2 1/9 0 Find F (1, –2) and F(3,3).! please solve ASAPProbabilities
- Suppose that the random variable, X, is a number on the biased die and the p.d.f. of X is as shown below; X 1 2 3 4 5 6 P(X=x) 1/6 1/6 1/5 k 1/5 1/6 a) Find; (i) the value of k. (ii) E(X) (iii) E(X2) (iv) Var(X) (v) P(1 X <5) b) If events A and B are such that they are independent, and P(A) = 0.3 with P(B) = 0.5; i. Find P(A n B) and P(AUB) ii. Are A and B mutually exclusive? Explain. c) In how many ways can the letters of the word STATISTICS be arranged?Two events A and B are such that: P ( A ) = 0.3, P ( B ) = 0.4 and P ( A U B ) =0.5 find P (AUB)(1) Let X be a random variable with p.d.f. ke 3 0(3) Let X be a random variable with p.d.f 2 (3x+6) 15 then E(x) is 11 12 (b) 30 (c) 30 (d) (e) None of these 33 7162. A random variable X has the following probability distribution. 1 2 3 4 5 6 7 8 f(X) k 2k 3k | 4k 5k 6k 7k 8k Find the value of, (i) ´k (ii) P(X<2) (iii) P(2If the random variable X denotes the real valued outcomes given in the following table with the given frequency of occurrence of each of the outcomes, fill in the last line of the table and find the expected value of X. Outcome -2 -1 0 1 2 Frequency 22 29 18 12 20 P(X) E(X) =2. A random variable|x has the following probability distribution. Find the value of p and then evaluate the following probabilities: P(X 5) and P(0 < X < 6). Find the mean of the probability distribution. 1 3 4 6 17 P(X) 2p 2p 3p p2 2p2 7p? + p Value of p = P(X < 5) =. P(X 2 5) = P(0 < X < 5) = Mean (u) =(1) Let X be a random variable with a function k(3x2 +6) f(x) =- -1,0,1,2 then O.w 1 1 1 (a) k = 44 (b) k =- 43 7 (c) k = 42 (d) k (e) None of these 44 a is the correct answer b is the correct answer O c is the correct answer d is the correct answer e is the correct answersolve part aSEE MORE QUESTIONSRecommended 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