Knewton Alta - Chapter 5 - Continuous Random Variables 2022

Document Content and Description Below

Knewton Alta - Chapter 5 - Continuous Random Variables 2022 The amount of time it takes Hugo to solve a Rubik's cube is continuous and uniformly distributed between 4 minutes and 11 minutes. What... is the probability that it takes Hugo less than 5 minutes given that it takes less than 6 minutes for him to solve a Rubik's cube? Provide the final answer as a fraction. - Uniform distribution - happens when each of the values within an interval are equally likely to occur, so each value has the exact same probability as the others over the entire interval givenA Uniform distribution may also be referred to as a Rectangular distribution Conditional probability - the likelihood that an event will occur given that another event has already occurred The amount of time it takes Evelyn to solve a Rubik's cube is continuous and uniformly distributed between 3 minutes and 12 minutes. What is the probability that it takes Evelyn more than 8 minutes given that it takes more than 4 minutes for her to solve a Rubik's cube? - Correct answer: 0.500 Let X be the time it takes to solve a Rubik's cube. The range of possible values is 3 to 12, so X∼U(3,12). We are given that it takes more than 4 minutes, so this means that the possible values are restricted to the range 4 to 12. This interval will help us write our probability density function (height of the rectangle). f(x)=1//12−4=18 We are interested in values greater than 8. So the range of desired outcomes is 8 to 12. This will be the length of our base, 12−8=4. The probability is the area of the shaded rectangle under the probability density function line, which is the product of the base and the height. So we find P(X>8∣∣X>4)=(12−8)(112−4)=(4)(18)=48=0.500 Lexie is waiting for a train. If X is the amount of time before the next train arrives, and X is uniform with values between 4 and 11 minutes, then what is the average (mean) time for how long she will wait? - Correct answers:$\text{mean=}7.5\text{min}$mean=7.5min The mean of a random variable with a uniform distribution U(a,b) is μ=a+b2 (this is the midpoint of the interval [a,b]). So in this case, a=4 and b=11, so the mean isa+b2=4+112=152=7.5So the average waiting time is 7.5 minutes. Lexie is waiting for a train. If X is the amount of time before the next train arrives, and X is uniform with values between 4 and 11 minutes, then what is the approximate standard deviation for how long she will wait, rounded to one decimal place? - Correct answers:$\text{std=}2.0\text{min}$std=2.0min CONTINUES... [Show More]

Last updated: 1 year ago

Preview 1 out of 44 pages