Let A be an event and Let S be the Sample Space. Prove that the probability function, P(A) = n(A) / n(S), satisfies the three axioms below. 1) P(Ai) > 0 2) P(S) = 1 3) P(U Ai) = (Summation of all values 'i') P(Ai)
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Let A be an
1) P(Ai) > 0
2) P(S) = 1
3) P(U Ai) = (Summation of all values 'i') P(Ai)
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- The probability mass function of a discrete random variable is: 7-x p(x) = a=) G) for x = 1,2,., 14 (a) Compute Pr{35) (c) Compute the expected value, the variance, and the standard deviation.3) A random variable X takes the values 0, 2 and 3 with probabilities 0.3, 0.1 and 0.6, respectively. A random variable in the form of Y = 3(X-1)2 is defined. a) Find the expected value and variance of the random variable X. b) Find the variance of the Y random variable. c) Find the cumulative distribution function of the Y random variable.Suppose a random variable z is best described by a uniform probability distribution with range 1 to 6. Find the value of a that makes the following probability statements true. (a) P(a ≤ a) 0.63 G= (b) P(r a) = 0.22 (0) P(2.03 ≤ ≤ a) = 0.01 a=
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- Suppose that X is a discrete random variable with the probability mass function given by: where i = 1,2,3 .8 36 a) Plot p(x) b) Compute and plot F(x) c) Compute (i) P (2.99992. 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) A merchant receives a shipment of five photocopying machines, two of which are defective. He randomly selects three of the machines and checks them for faults. Let the random variable X be number of faulty machines in his selection. Find the probability distribution of random variable X in the table form. b) Let X be the random variable with the cumulative probability distribution: x < 0 F(x)=kx² 1 0Let X be a random variable that can take values x = 2,4,6,8 and has probabilities given by the function P(X = x) = 3x/60 Find (1) P(X = 4) (2) P (X ≤ 6) (3) P(X < 6) (4) P (X ≥ 3)there is small parking lot behind a Floral Shop that has two parking lot spaces. Let X be the number of cars parked in the parking lot at midday. The probability distribution of X is given by P(X=x)= 4-x x=0 1 2 9 (i) Construct the probability distribution table (ii) What is the probability that there will be at most 1 car in the parking lot? (iii) Calculate the expected number of cars in the parking lot at middayRecommended 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