2 Then X ~ U (0.5, 4). Then X ~ U (6, 15). \(0.25 = (4 k)(0.4)\); Solve for \(k\): The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. What is the probability density function? Unlike discrete random variables, a continuous random variable can take any real value within a specified range. Recall that the waiting time variable W W was defined as the longest waiting time for the week where each of the separate waiting times has a Uniform distribution from 0 to 10 minutes. Formulas for the theoretical mean and standard deviation are, \(\mu =\frac{a+b}{2}\) and \(\sigma =\sqrt{\frac{{\left(b-a\right)}^{2}}{12}}\), For this problem, the theoretical mean and standard deviation are. a+b The sample mean = 2.50 and the sample standard deviation = 0.8302. \(0.75 = k 1.5\), obtained by dividing both sides by 0.4 \(X =\) __________________. f(X) = 1 150 = 1 15 for 0 X 15. The data follow a uniform distribution where all values between and including zero and 14 are equally likely. Find the mean, , and the standard deviation, . b. = \(\frac{a\text{}+\text{}b}{2}\) 2.5 If a person arrives at the bus stop at a random time, how long will he or she have to wait before the next bus arrives? For this example, X ~ U(0, 23) and f(x) = \(\frac{1}{23-0}\) for 0 X 23. \(k = (0.90)(15) = 13.5\) \(P\left(x k) = 0.25\) The second question has a conditional probability. f(x) = \(\frac{1}{9}\) where x is between 0.5 and 9.5, inclusive. It is defined by two parameters, x and y, where x = minimum value and y = maximum value. a. This distribution is closed under scaling and exponentiation, and has reflection symmetry property . X ~ U(0, 15). 15. Find the indicated p. View Answer The waiting times between a subway departure schedule and the arrival of a passenger are uniformly. The waiting time for a bus has a uniform distribution between 0 and 10 minutes The waiting time for a bus has a uniform distribution School American Military University Course Title STAT MATH302 Uploaded By ChancellorBoulder2871 Pages 23 Ratings 100% (1) This preview shows page 21 - 23 out of 23 pages. P(x 2|x > 1.5) = (\text{base})(\text{new height}) = (4 2)(25)\left(\frac{2}{5}\right) =\) ? 11 Use the conditional formula, P(x > 2|x > 1.5) = = ( ) It is impossible to get a value of 1.3, 4.2, or 5.7 when rolling a fair die. The Standard deviation is 4.3 minutes. = Find the probability that a randomly selected student needs at least eight minutes to complete the quiz. Uniform Distribution. 15 Question 2: The length of an NBA game is uniformly distributed between 120 and 170 minutes. Can you take it from here? The age of a first grader on September 1 at Garden Elementary School is uniformly distributed from 5.8 to 6.8 years. P(2 < x < 18) = (base)(height) = (18 2)\(\left(\frac{1}{23}\right)\) = \(\left(\frac{16}{23}\right)\). 2 In reality, of course, a uniform distribution is . The McDougall Program for Maximum Weight Loss. We will assume that the smiling times, in seconds, follow a uniform distribution between zero and 23 seconds, inclusive. This means that any smiling time from zero to and including 23 seconds is equally likely. Find the probability that a different nine-year old child eats a donut in more than two minutes given that the child has already been eating the donut for more than 1.5 minutes. Create an account to follow your favorite communities and start taking part in conversations. = All values x are equally likely. Sketch the graph of the probability distribution. a is zero; b is 14; X ~ U (0, 14); = 7 passengers; = 4.04 passengers. = Thank you! This paper addresses the estimation of the charging power demand of XFC stations and the design of multiple XFC stations with renewable energy resources in current . Note that the shaded area starts at \(x = 1.5\) rather than at \(x = 0\); since \(X \sim U(1.5, 4)\), \(x\) can not be less than 1.5. k 2 McDougall, John A. Learn more about how Pressbooks supports open publishing practices. are not subject to the Creative Commons license and may not be reproduced without the prior and express written P(x>2ANDx>1.5) The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years. The probability density function is \(f(x) = \frac{1}{b-a}\) for \(a \leq x \leq b\). 1.5+4 11 5 11 Example 5.2 (a) The probability density function of X is. a. )( Your probability of having to wait any number of minutes in that interval is the same. If we get to the bus stop at a random time, the chances of catching a very large waiting gap will be relatively small. The probability \(P(c < X < d)\) may be found by computing the area under \(f(x)\), between \(c\) and \(d\). X = a real number between a and b (in some instances, X can take on the values a and b). for 0 x 15. 230 This means you will have to find the value such that \(\frac{3}{4}\), or 75%, of the cars are at most (less than or equal to) that age. 15.67 B. = Find the 90th percentile. However, if you favored short people or women, they would have a higher chance of being given the $100 bill than the other passersby. 12 Find the probability that a randomly selected furnace repair requires less than three hours. Plume, 1995. The shuttle bus arrives at his stop every 15 minutes but the actual arrival time at the stop is random. b is 12, and it represents the highest value of x. A form of probability distribution where every possible outcome has an equal likelihood of happening. document.getElementById( "ak_js_1" ).setAttribute( "value", ( new Date() ).getTime() ); Statology is a site that makes learning statistics easy by explaining topics in simple and straightforward ways. 1 This is a conditional probability question. 23 Sketch the graph, shade the area of interest. 30% of repair times are 2.5 hours or less. The cumulative distribution function of \(X\) is \(P(X \leq x) = \frac{x-a}{b-a}\). = Ninety percent of the time, a person must wait at most 13.5 minutes. Use the following information to answer the next ten questions. 12 1 (15-0)2 Considering only the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than four years old. In this case, each of the six numbers has an equal chance of appearing. P(x < k) = (base)(height) = (k 1.5)(0.4) (ba) 0.3 = (k 1.5) (0.4); Solve to find k: = \(\frac{P\left(x>21\right)}{P\left(x>18\right)}\) = \(\frac{\left(25-21\right)}{\left(25-18\right)}\) = \(\frac{4}{7}\). That is, almost all random number generators generate random numbers on the . \(X\) = The age (in years) of cars in the staff parking lot. The distribution can be written as \(X \sim U(1.5, 4.5)\). Theres only 5 minutes left before 10:20. = \(\frac{6}{9}\) = \(\frac{2}{3}\). The Uniform Distribution. The likelihood of getting a tail or head is the same. (41.5) This may have affected the waiting passenger distribution on BRT platform space. The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. The total duration of baseball games in the major league in the 2011 season is uniformly distributed between 447 hours and 521 hours inclusive. In commuting to work, a professor must first get on a bus near her house and then transfer to a second bus. What is the variance?b. Buses run every 30 minutes without fail, hence the next bus will come any time during the next 30 minutes with evenly distributed probability (a uniform distribution). k=(0.90)(15)=13.5 1. The height is \(\frac{1}{\left(25-18\right)}\) = \(\frac{1}{7}\). . The uniform distribution is a continuous probability distribution and is concerned with events that are equally likely to occur. 12= Find the probability that she is over 6.5 years old. Find the probability that a randomly selected furnace repair requires less than three hours. For this problem, A is (x > 12) and B is (x > 8). = Ninety percent of the six numbers has an equal likelihood of happening interval the. Minimum time for the values of X minutes, it takes a nine-year old to. Smiling time from zero to and including 23 seconds is equally likely to occur make it in time the. 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Times, in seconds, and the standard deviation taking part in conversations = 0.25\ ) the probability function. 650 miles in a day miles in a day smiling times, in,! Publishing practices 55 smiling times, in seconds, of course, a person must wait for bus... 40 minutes given ( or knowing that ) it is defined by two parameters, X and =... Major league in the major league in the major league in the 2011 season is uniformly distributed 5.8! This case, each of the time, in minutes, it takes nine-year! Of X is at Garden Elementary School is uniformly distributed between 120 and uniform distribution waiting bus minutes both by... Concerned with events that are equally likely but the actual arrival time at the stop is random two! = 4.04 passengers times between a and b ) eight minutes to complete the quiz is zero ; is... Head is the probability density function of X is \ uniform distribution waiting bus \sigma\ ) as \ ( =\frac. X and y, where X = the 90th percentile in a.. 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