Question

Where's the bus? Sally takes the same bus to work every morning. Let X = the amount of time (in minutes) that she has to wait for the bus on a randomly selected day. The probability distribution of X can be modeled by a uniform density curve on the interval from 0 minutes to 8 minutes. Define the random variable V=60X.

Answer 1

The random variable represents the amount of time a commuter must wait for a subway train to arrive during rush hour, following a uniform distribution on the interval from 0 to 8 minutes.

Step-by-step explanation:

a. Define the random variable.

The random variable, X, represents the amount of time that a commuter must wait for a train to arrive during rush hour.

b. Define the distribution of X.

The distribution of X is a uniform distribution, where the train arrives every eight minutes, so X has a uniform probability distribution on the interval from 0 to 8 minutes.

Answer 2

The random variable X represents the amount of time Sally has to wait for the bus in minutes. The random variable V is defined as V = 60X, representing the amount of time Sally has to wait for the bus in hours. The probability distribution function for X is a uniform density function on the interval from 0 minutes to 8 minutes, with a probability density function of 1/8 for 0 ≤ x ≤ 8.

Step-by-step explanation:

The question is asking about a probability distribution of the amount of time Sally has to wait for the bus on a randomly selected day. The distribution can be modeled by a uniform density curve on the interval from 0 minutes to 8 minutes. The random variable V is defined as V = 60X, where X is the time Sally has to wait for the bus in minutes. This means that the random variable V represents the amount of time Sally has to wait for the bus in hours.

To find the probability distribution function, we need to find the probability density function for X. Since X follows a uniform distribution, the probability density function is a constant value on the interval from 0 to 8 minutes. Therefore, the probability density function f(x) is equal to 1/8 for 0 ≤ x ≤ 8.

The random variable for this question is X

represents the amount of time Sally has to wait for the bus in minutes. The random variable V is defined as V = 60X, which represents the amount of time Sally has to wait for the bus in hours. The probability distribution function for X is a uniform density function on the interval from 0 minutes to 8 minutes, and the probability density function for X is 1/8 for 0 ≤ x ≤ 8.