A discrete random variable X has the range Rx = {-1,1.1, 2.2, 3.4}. The probability mass function p(x) of X is given in the table below: -1 1.1 2.2 3.4 p(x) a 2a 0.1 0.3 Find the value of a. a =
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- Suppose a discrete random variable W has the following probability mass function (where c > 0 is a constant): w 1 2 3 5c p(w) 20 4 2 4 (a) What is the value of c? (b) Find the standard deviation of W.The probability density function of a discrete random variable X is given by the following table: Px(X = 1) = .05 Px(X = 2) = .10 Px(X = 3) = .12 Px(X = 4) = .30 Px (X = 5) = .30 Px (X = 6) = .1i Px (X = 7) = .01 Px(X = 8) = .01 i) Compute E(X). ii) Compute Var(X). iii) Compute Px(X 3)1. Determine the constant c so that the function p(x) = 0(x) defines the probability den- sity for a random variable {. Then find the cumulative distribution function and the mean of {. %3D
- 52 l l 0.5 If P(A/B)=0.5 and P(B)=0.8, then the 1/1 probability that both A and B occur is O 0.8 O 0.2 O 0.6 0.4 If f(x)=(2x+3)/1O, where 0A 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 11/12Q1 Let probability distribution function of Xbe defined by х %3D 0,1, 2, 3. a P(x) = otherwise. Find the value of a. (а) (b) (c) (d) Find P(-1A screening test for a particular infectious disease shows a positive test result in 90% of all cases when the disease is actually present, and in 10% of all cases when it is not. Assume that t% of the population is infected, where t is = 1. For a randomly chosen from the population person, find the probability that the person is actually infected if the test shows positive.O Prove that E(X) = E(X/Y), where X and Y are two random variables which are independent. %DDetermine the value of c such that the function is a probability mass function. g= {(11,0.12), (13,0.4c), (15,0.4c), (17,0.22)} ... C = (Simplify your answer.)The possible values of a discrete random variable X are 0, 1, 3, and 6 with respective probabilities 0.2, 0.3, 0.1, 0.4. Find E[X] and Var(X).The probability density function of X discrete random variable given in the photograph is given. Find the expected value, variance and standard deviation of X.a.2 b.-1 c.0 d.-2 e.1Recommended 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