. What is the probability that X is greater than 5? b. Find the cumulative distribution function F(x) (P(X ≤ x)) for x between 0 and 10
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a. What is the
b. Find the cumulative distribution
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- 3 Determine whether the following is a valid distribution function F(X) =1-e2 for x2 0 elsewhereQ8. 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 abovePlease see attached image...
- Let 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…The following function is a cumulative distribution function. x < -10 0.1510Explain the steps if you canSTAT 202: Individual Assignment x>0 1. Given the Gamma distribution as f(x) =- elsewhere Find the mean and variance of the distribution. 2a. Suppose that a large conference room for a certain hotel can be reserved for no more than 4 hours. However, the use of the conference room is such that both long and short conferences occur quite often. In fact, it can be assumed that length X of a conference has a uniform distribution on the interval [0, 4]. i. Determine the probability density function ii. What is the probability that any given conference last at least 3 hours? b. A cement wholesale distributor has a large store that hold fixed supplies and are filled every Sunday. Of interest to the wholesaler is the proportion of this supply that is sold during the week. Over many weeks of observation, the distributor found out that this proportion could be modeled by a beta distribution with a = 4 and ß = 2 . Find the probability that the wholesaler will sell at least 90% of his stock in a…1 Events X and Y are such that P(x)=0.35 and P(x or y)=0.80. Given that X and Y are independent and non‐mutually exclusive, determine p(y). Give your finalanswer as a percentage to two decimal places.Let X-T(4) and Y~ x2 (4). The following plot depicts the cumulative distribution functions of X and Y. We don't know which is which. The horizontal lines have values 25% and 75%. We denote by q1 the x-coordinate correponding to the red point and by q2 the x-coordinate corresponding to the blue point. Which of the following statements are true? 1.00 - 0.75 0.50 - 0.25+ 0.00 - The answer is : The cdf of X corresponds to the red curve while the one of Y corresponds to the blue curve. Can you explain why? DensityIf X is distributed t2s then what is the probability X is less than or equal to 1.7(Pr (X ≤ 1.70))? 0.70 0.92 0.05 0.952..You are given fT(30)(t) = t/1250 0≤t<50 0 o.w. a) Find the probability that (30) dies between ages 40 and 45. b) Find the probability that (60) dies between ages 65 and 85. c) Define the cumulative distribution function of T (45). d) Define the force of mortality of T (50).The central limit theorem says that: lima to0 P[ < æ] = ® (x)Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
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