t) P (X > s + t) P (X > t) e−λ(s+t) e−λt e−λs P (X > s) – Example: Suppose that the amount of time one spends in a bank is exponentially distributed with mean 10 minutes‚ λ = 1/10. What is the probability that a customer will spend more than 15 minutes in the bank? What is the probability that a customer will spend more than 15 minutes in the bank given that he is still in the bank after 10 minutes? Solution: P (X > 15) = e−15λ = e−3/2 = 0.22 P (X > 15|X > 10) = P (X > 5) = e−1/2 =
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PROBABILITY QUESTIONS Q1). You draw a card at random from a standard deck of 52 cards. Neither you nor anyone else looked at the card you picked. You keep it face down. Your friend then picks a card at random from a remaining 51 cards. a) What is the probability that your card is ace of spades? 1/52 b) What is the probability that your friend’s card is ace of spades? (Hint: Construct the sample space for what your friend’s card can be.) 1/51 c) You turn over your card and it is 10 of
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True/False Questions 1. The standard deviation of any normal random variable is always equal to one. Answer: False Type: Concept Difficulty: Easy 2. For any normal random variable‚ the probability that the random variable will equal one is always zero. Answer: True Type: Concept Difficulty: Medium 3. The graph of a standard normal random variable is always symmetric. Answer: True Type: Concept Difficulty: Easy 4. The formula will convert any normal
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Karan negi 12.2 12.3 We use equation 2 to find out probability: F(t)=1 – e^-Lt 1-e^-(0.4167)(10) = 0.98 almost certainty. This shows that probability of another arrival in the next 10 minutes. Now we figure out how many customers actually arrive within those 10 minutes. If the mean is 0.4167‚ then 0.4167*10=4.2‚ and we can round that to 4. X-axis represents minutes (0-10) Y-axis represents number of people. We can conclude from this chart that the highest point with the most visitors
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Hadley Smith uses indirect and direct characterization to evince how Hadley is a clumsy and unlucky person. Hadley first reveals her clumsy sides by forgetting her stuff‚ making everything drop on the floor or being late for her plane. Not only she misses her plane‚ but she also has to sleep in a tiny airport chamber‚ being claustrophobic. Smith says “Or later: if she hadn’t given herself a paper cut while printing out her ticket‚ if she hadn’t lost her charger‚ if there hadn’t been traffic on the
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bagel. (a) Find the probability distribution for X. (b) Suppose at least 3 people buy a plain bagel. What is the probability that exactly 4 people buy a plain bagel? 3. The probability distribution for a discrete random variable X is given by the formula p(r) = for r = 1‚ 2‚ . . . ‚ 6. (a) Verify that this is a valid probability distribution. (b) Find P (X = 4). (c) Find P (X > 2). (d) Find the probability that X takes on the value 3 or 4. (e) Construct the corresponding probability histogram. 4. Two
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relationship of how the probability of infection affects the people in the village when it is increased or decreased. This will determine whether the people in the village die or not from the epidemic. As the probability of infection is increased‚ the more people in the village will die. This is because the villagers are more likely to contract the disease‚ putting them at a higher risk of dying to the epidemic. As an example more people will survive in the village if the probability of infection is 20%
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Subject CT3 Probability and Mathematical Statistics Core Technical Syllabus for the 2014 exams 1 June 2013 Subject CT3 – Probability and Mathematical Statistics Core Technical Aim The aim of the Probability and Mathematical Statistics subject is to provide a grounding in the aspects of statistics and in particular statistical modelling that are of relevance to actuarial work. Links to other subjects Subjects CT4 – Models and CT6 – Statistical Methods: use the statistical concepts
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Descriptive Statistics and Probability Distribution Problem Sets Emily Noah QNT561 Anthony Matias December 24‚ 2012 Descriptive Statistics and Probability Distribution Problems Sets Descriptive statistics and probability distribution is two ways to find information with certain data giving. In Descriptive statistics the data can give a mode‚ mean‚ median‚ and range by the numerical information‚ which is giving to find the information. In probability distribution the data is collected and
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Course paper in Philosophy of Science and Ethics Title: The relevance of Statistics and Probability for the study of the thermodynamics properties (The Maxwell-Boltzmann Theory) Abstract There are many philosophical debates as to the appropriateness of the use of statistics and probability as scientific research measures. Many renowned philosophers believe that since scientific investigation aims at the ultimate goal of presenting truth about the observations and processes in our universe
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