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Which of the following represents a valid probability distribution for a discrete variable? outcomes 2 3 4 5 6 1. probability 0.1 0.3 0.3 0.2 0.1 outcomes 1 2 3 4 5 2. probability 0.3 0.2 0.2 0.2 0.2 C A) Only 1. B) Only 2. C) Both 1. and 2. D) None O E) We don't have enough data to tellConsider the 3 independent random variables X ~ Bernoulli(0.5); Y ~ Bernoulli(0.3); S ~ Bernoulli(0.4) Then A) The variance of X - Sis 0.1 O B) The variance of X - Y is 0.8 O C) The variance of X - Y is 0.04 O D) The variance of S - Y is 0.45 C E) None of the aboveThe table below reports several values of the cumulative distribution function (cdf) of the continuous random variable X. What is the probability that X is between 2 and 6? A) 0.246 B) 0.648 C) 0.473 D) 0.922 E) None of the above We have a folder containing 20 movies. Below are the summary statistics for the sizes (in GB) of the movies. If the size of each movie increases by 168, how would the summary statistics change? Mean Median SD 4.28 4.54 2.15 A) The mean, the median and SD would all increase by 168. B) The mean and median would increase by 163, and the SD would remain the same. C) The mean and SD would increase by 168, and the median would remain the same. D) The mean and median would remain the same, and the SD would increase by 163. E) None of the above. You are conducting a test of hypothesis and set the signicance level to a = 0.05. This means that: A) The probability that you reject the null hypothesis is a = 0.05 B) The probability that you fail to reject the null hypothesis is or = 0.05 C) The probability that you fail to reject the null hypothesis when the null is true is a = 0.05 D) The probability that you reject the null hypothesis when the null is true is a = 0.05 E) None of the above Bank ABC has two call centers: 0 The waiting time at Baltimore call center is normally distributed, with mean 20 minutes and standard deviation 4 minutes. 0 The waiting time at DC call center is normally distributed, with mean 21 minutes and standard deviation 3 minutes. Which call center has the larger probability that the waiting time is more than 24 minutes? A) Baltimore B) DC C) The two probabilities are the same D) It cannot be determined without additional information