5) A man aiming at a target receives 10 points if his shot is within 1...
Problem 1. Arrows shot hit at random a circular target of radius 10 cm. (a) What is the probability that a shot will fall within a circle of radius 5 cm? The second circle fits entirely inside the target. (b) What is the probability that a shot wil fall within a square with sides of length 2 cm? The square fits entirely inside the target
Problem 1. (12 Points) A point is uniformly distributed within the disk of radius 1. That is, its density is (a) find the probability that its distance from the origin is less than k, 0 Sk1 (b) determine P(x<Y). (c) determine P(X +Y < 0.5)
a) 3. [10 Points] A student usually receives ten text messages within the lunch hour in a weekday. Consider a 30 minutes' period in a week day lunch. What the probability that he receives no more than 5 messages during that time period? b) What is the probability that he receives more than 5 and less than 15 messages during that time? c) What is the probability that he receives at least 8 test messages during that time period? d)...
(1 point) Two points are selected randomly on a line of length 10 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distributed over [0,5) and Y is uniformly distributed over (5, 10]. Find the probability that the distance between the two points is greater than 2. answer:
Previous Problem Problem List Next Problem (1 point) A man and a woman agree to meet at a cafe about noon. If the man arrives at a time uniformly distributed between 11:40 and 12:10 and if the woman independently arrives at a time uniformly distributed between 11:55 and 12: 35, what is the probability that the first to arrive waits no longer than 5 minutes? 1/3 Preview My Answers Submit Answers
(1 point) Two points are selected randomly on a line of length 16 so as to be on opposite sides of the midpoint of the line. In other words, the two points X and Y are independent random variables such that X is uniformly distriuted over [0,8) and Y is uniformly distributed over (8,16] Find the probability that the distance between the two points is greater than 6. P(|X – Y| > 6) =
(3 pts) The lengths of the sardines received by a certain cannery are normally distributed with mean 4.62 inches and a standard deviation 0.23 inch. What percentage of all these sardines is between 4.35 and 4.85 inches long? (3 pts) Suppose that the weight (X) in pounds, of a 40-year-old man is a normal random variable with standard deviation σ = 20 pounds. If 5% of this population is heavier than 214 pounds what is the mean μ of this...
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Problem 4. A circular-shaped archery target has three concentric circles painted on it. The in- nermost circle has a radius of 1/V3 feet, the middle has a radius of 1 foot, and the outermost circle has a radius of v3 feet. An arrow hitting in the innermost circle counts for 4 points, between the in nermost and middle circle 3 points, between the middle and outermost circle 2 points, and not hitting...
1) Rate data often follow a lognormal distribution. Average power usage (dB per hour) for a particular company is studied and is known to have a lognormal distribution with parameters μ = 4 and σ = 2. What is the probability that the company uses more than 270 dB during any particular hour? 2) A certain type of device has an advertised failure rate of 0.01 per hour. The failure rate is constant and the exponential distribution applies. (a) What...
D Question 5 10 pts A geologist is attempting to measure the distance between two mountain peaks by taking the average of a series of measurements. Each measurement X, is an ii.d. random variable with mean d and variance of 10 inches. Using Chebyshev's inequality, how many measurements must the geologist make in order to be 99% certain that the value he obtains is within 1/4 inch of the actual distance? O n 100,000 On 23,200 O n 250,000 On...