Chapter 3 Probability Distributions 1. Based on recent records‚ the manager of a car painting center has determined the following probability distribution for the number of customers per day. Suppose the center has the capacity to serve two customers per day. |x |P(X = x) | |0 |0.05 | |1 |0.20 | |2 |0.30 | |3 |0.25 | |4 |0.15 | |5 |0.05 | a. What is the probability that one
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Math 107 002 Homework 5 (due 13 Oct 2011) Fall 2011 Please use your calculators and give your final answers to 3 significant figures. Show your work for full credit. Please state clearly all assumptions made. 1. Classify each random variable as discrete or continuous. (a) The number of visitors to the Museum of Science in Boston on a randomly selected day. (b) The camber-angle adjustment necessary for a front-end alignment. (c) The total number of pixels in a photograph produced by a digital camera
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Show that if the uniform variable x has an Erlang density with n=2‚ then Fx(x) = (1-e-cx-cxe-cx) U(x) Q 4-8‚ The random variable x is N (10; 1)‚ Find f (x | (x-10)2 <4) Q 4-9‚ Find f(x) if F(x) = (1-e-ax) U(x-c). Q 4-10‚ If x is N (0‚ 2) find a) P{1≤ x ≤ 2} b) P{1≤ x ≤2 | x ≥ 1} Q4-14‚ A fair coin is tossed 900 times and the random variable x equals the total number of heads. a) Find fx(x)‚ 1: exactly‚ 2: approximately Gamma Distribution eq. b) Find P {435
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Probability distribution Definition with example: The total set of all the probabilities of a random variable to attain all the possible values. Let me give an example. We toss a coin 3 times and try to find what the probability of obtaining head is? Here the event of getting head is known as the random variable. Now what are the possible values of the random variable‚ i.e. what is the possible number of times that head might occur? It is 0 (head never occurs)‚ 1 (head occurs once out of 2 tosses)
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What is mean‚ variance and expectations? Mean - The mean of a discrete random variable X is a weighted average of the possible values that the random variable can take. Unlike the sample mean of a group of observations‚ which gives each observation equal weight‚ the mean of a random variable weights each outcome xi according to its probability‚ pi. The mean also of a random variable provides the long-run average of the variable‚ or the expected average outcome over many observations.The common symbol
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STA1101 Normal Distribution and Continuous random variables CONTINUOUS RANDOM VARIABLES A random variable whose values are not countable is called a _CONTINUOUS RANDOM VARIABLE._ THE NORMAL DISTRIBUTION The _NORMAL PROBABILITY DISTRIBUTION_ is given by a bell-shaped(symmetric) curve. THE STANDARD NORMAL DISTRIBUTION The normal distribution with and is called the _STANDARD NORMAL DISTRIBUTION._ Example 1: Find the area under the standard normal curve between z = 0 and z = 1.95 from z
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Modelling 2 Week 3: Discrete Random Variables Stephen Bush Department of Mathematical Sciences MM2: Statistics - Week 3 - 1 Random Variables • Reference: Devore § 3.1 – 3.5 • Definitions: • An experiment is any process of obtaining one outcome where the outcome is uncertain. • A random variable is a numerical variable whose value can change from one replicate of the experiment to another. • Sample means and sample standard deviations are random variables • They are different from
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3 .0 out of 5 points The drying rate in an industrial process is dependent on many factors and varies according to the following distribution. What is the probability that a drying time will be at most 5 minutes? Answer Selected Answer: .44 . Question 4 .0 out of 5 points A fair coin is tossed 10 times. What is the probability that a tail will be observed at least 4 times? Round your answer to four places after the decimal. Answer Selected Answer: .5006
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continuous random variable because the time is being measured. All possible results for the variable time (t) would be greater than > 0. b) The weight of a T-bone steak is a continuous random variable because the weight of the steak is measured. All the possible results for the weight of the T-bone steak would be positive numbers making the variable weight (w) > greater than 0. c) The number of free throw attempts before the first shot is made is a discrete random variable
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WHAT IS A RANDOM VARIABLE? A random variable assigns a number to each outcome of a random circumstance‚ or‚ equivalently‚ a random variable assigns a number to each unit in a population. It is easier to create rules for broad classes of situations and then identify how a specific example fits into a class than it is to create rules for each specific example. We can employ this strategy quite effectively for working with a wide variety of situations Involving probability and random outcomes. We
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