A random variable X is defined by the CDF if x <0 = 1 Fx (x) = { x, if 0 < x < 1 K, if x >1 0, Answer the following: a) Find the value of K b) What is the probability that 0.5 < Xs 1? c) What is the probability that X exceeds 2?
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- In the mid-afternoon a restaurant receives orders such that the time between them follows an exponential distribution. The mean time between orders is 11 minutes. a) What is the probability that the restaurant receives no orders in a 30-minute interval? b) What is the probability that the restaurant receives at least one other order within 1 min of the first one?Suppose that a point is randomly chosen from a segment with a length of 12 units. What is the probability that no of two smaller segments is smaller than 2/3 units? ROUND OFF your answer in DECIMAL FORM (4 decimal places)Which of the following is a continuous random variable? A)The number of students arrives to the library checkout desk before noon time. B)The number of students waiting in the cafeteria lane for lunch. C)The travel time of a bus between two cities. D)The number of newspapers sold on a specific date. E)The number phone calls received by call center for a certain period of time.
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- Assume that when human resource managers are randomly selected, 56% say job applicants should follow up within two weeks. If 5 human resource managers are randomly selected, find the probability that at least 3 of them say job applicants should follow up within two weeks. The probability is ☐ (Round to four decimal places as needed.)It is known that 37% of new freshmen at State University will graduate within 6 years. Suppose we take a random sample of n=70 new freshmen at State University. Let X = the number of these sampled freshmen who graduate within 6 years. (Do not use a normal approximation for this problem. This is a binomial problem.) a) What is the probability that X < 29? b) What is the probability that 28 ≤ x ≤ 31? c) What is the probability that X = 31? d) What is the expected value of X? e) What is the variance of X?