Show that the following distribution is a probability mass function. Construct a plot of the probability mass function and obtain the cumulative probability function. P(X = -2) = 0.2, P(1 < X < 3) = 0.1, P(X = 4) = 0.2, P(5 < X < 5.5) = 0.2, P(X = 6) = 0.15, P(7 < X < 8) = 0.15 %3D
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- Let x be the number of potential weapons detected by a metal detector at an airport on a given day. The following table lists the probability distribution of x. 1 | 2 3 4 P(x) | 0.14 0.28 0.22 0.21 | 0.15 (a) Calculate the mean and standard deviation for this probability distribution (b) Verify that P(x) is a probability distribution function and calculate P(x 3)A cable company advertises short wait times for customer service calls. The graph shows the wait times (in seconds) for a sample of customers. Based on the data given, if a customer is selected at random, find the probability that Number of Customers vs. Wait Time, x 120 sx< 150 x< 30 90 sx< 120- 60 sx<90 5 15 32 21 30 sx< 60 a. The customer will wait less than 30 sec. b. The customer will wait at least 30 sec. C. The customer will wait at least 90 sec but less than 120 sec. d. The customer will wait more than 150 sec. 2.Suppose the probability density function for a uniform distribution ranging from 0 to 1. Thus the probability that the random variable X is between 0.20 to 0.70 is
- Q8. In the casino game roulette, the probability of winning with a bet on red is 0.5. Let X be the number of winning bets out of 64 independent bets that are placed. Let Ø be the cumulative distribution function of the standard normal distribution. Find approximately P(X = 32), using the central limit theorem. (A) 0 (B) 0.5 (C) 20 (1)-1 (D) 20()-1 (E) None of the aboveDefine the t distribution of meansThe probability distribution of y, the number of accidents per 10 days of a diversion road in continuous days, is given by 1 3 4 f(y) 0.40 0.30 0.15 0.05 0.10 a. What is the probability of 1Given the probability density function f(x) = over the interval [2, 7], find the expected value, the mean, 5 the variance and the standard deviation. Expected value: Mean: Variance: Standard Deviation: > Next QuestionThe probability distribution for X and Y is shown by the table. Find the marginal distribution function value of X = 1. G(1) = X 2 3 1 0.06 0.10 0.04 2 0.10 0.12 0.13 3 0.15 0.19 0.11 YLet X have an exponential distribution with 0-1. The probability P 6. <5is equal toX P[X = X] 1.195 0.197 1.481 0.181 1.767 0.129 2.053 0.037 2.339 0.124 2.625 0.332 Consider the probability distribution table above. Determine the following: P[X = 1.481] : = F(2.053) = E[X] = Standard DeviationLet X be the number of bathrooms in a randomly selected house for sale in Malibu, California. Suppose X has the following probability distribution, where p(x) is the probability mass function, and F(x) is the cumulative distribution function. x 1 2 3 4 5 6 p(x) .05 .20 .32 .27 .10 .06 F(x) .05 .25 .57 a .94 1 a. What is the value of a? b. Calculate the probability that X < 3. c. Calculate the expected value of X. d. Calculate the variance of X. e. Calculate the expected value of x0.37 <_>f. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that each of the 3 selected houses has exactly 3 bathrooms? g. We randomly and independently select 3 different houses for sale in Malibu. What is the probability that exactly two of the selected houses have exactly 2 bathrooms ? h. Malibu has a water crisis. The town board will solve this crisis by charging a special…Exercise 1 Suppose that X has a continuous uniform distribution over the interval 7.3SEE MORE QUESTIONSRecommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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