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- W is a random variable with probabilities for w= 0,1 P(W = w) = {2h + k for w= 2 %3D 3k for w= 3,4 7 find the values of h and k. 10 (а) If P(W <2) = (b) Construct a probability distribution table for W. 4.3. A random variable X has the following probability distribution: 2 3 2k 3k 2K² Find (1) k, (ii) P(X 5), and (iv) P(0 ≤x≤ 5) PIA 7 4k² 3071. Consider the following probability distribution for the continuous random variable, X. 1 حا 4 5 X a. Find P(2 < X<4) (4-2) 4-10.9= 0.5 b. Find P(4 < X <5) 50.25 6= 0.25 c. Find P(X<4) -3.0
- 13. A continuous random variable is uniformly distributed between 200 and 220. a. What is the probability a randomly selected value will be greater than 215? b. What is the probability a randomly selected value will be less than 205? c. What is the probability a randomly selected value will be between 205 and 215? a. P(x > 215) = (Simplify your answer.) b. P(x< 205) = (Simplify your answer.) c. P(20510. Two random variables X and Y take on the values i and 2 with probability 1/2' (i = 1,2, ...). Show that the probabilities sum to one. Find the expected value of X and Y.5. The probability distribution of discrete random variable X is given by k for x = 1, 2, 3 x +1 P(X = x) %3D21:18 64 | 30ll a O 100 JO Imssb1.mutah.edu.jo/m Number of sales of household appliances, Y, makes in a day is given by following probability distribution. y: 3 4 p(y) : 0.10 0.28 0.18 0.11 0.16 0.17 Expected value of (2Y -3): Select one: а. 1.41 b. 1.45 c. 1.92 d. 2.46 e. None of These +2. The following probabilities are given for a certain life: 10P75 = 0.55, 20 P60 = 0.35, and = 0.65 15P 60 Evaluate (i) the probability that the life aged 60 will die between ages 75 and 85. (i the probability that the life aged 60 will die within age 80.2. The number of meteors found by a radar system in any 30-second interval under specified a. What is the probability that at least one meteor is found in a one-minute interval? ne meteors appear randomly b. Determine x such that the probability no meteor is found in x-minute interval is 0.02. UTM M UTM UTM c. If there is no meteor appear after two-minute interval, what is the probability that it UTM will appear in the next one and a half-minute interval? m UTMRecommended 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