1. The discrete random variable $X$ is the number of passengers waiting at a bus stop. The table below shows the probability distribution for $X$. What is the expected value $E(X)$ for this distribution? $X$ $P(X)$ 0 .20 1 .40 2 .30 3 .10 Total 1.00 A. 1.1 B. 1.3 C. 1.7 D. 1.9
Added by Amy M.
Close
Step 1
The expected value $E(X)$ of a discrete random variable $X$ is calculated by summing the product of each possible value of $X$ and its corresponding probability. The formula is: $E(X) = \sum [x \cdot P(X=x)]$ Show more…
Show all steps
Your feedback will help us improve your experience
Aarti Kumari and 52 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
A bus comes by every 10 minutes. The times from when a person arives at the busstop until the bus arrives follows a Uniform distribution from 0 to 10 minutes. A person arrives at the bus stop at a randomly selected time. Round to 4 decimal places where possible. a. The mean of this distribution is b. The standard deviation is c. The probability that the person will wait more than 5 minutes is d. Suppose that the person has already been waiting for 1.2 minutes. Find the probability that the person's total waiting time will be between 1.9 and 4.3 minutes e. 52% of all customers wait at least how long for the train? minutes.
Aarti K.
A municipal bus company has started operations in a new subdivision. Records were kept on the numbers of riders on one bus route during the early-morning weekday service. The accompanying table shows proportions over all weekdays. $$ \begin{array}{lcccccccc} \hline \text { Number of riders } & 20 & 21 & 22 & 23 & 24 & 25 & 26 & 27 \\ \hline \text { Proportion } & 0.02 & 0.12 & 0.23 & 0.31 & 0.19 & 0.08 & 0.03 & 0.02 \\ \hline \end{array} $$ a. Graph the probability distribution. b. Calculate and graph the cumulative probability distribution. c. What is the probability that on a randomly chosen weekday there will be at least 24 riders from the subdivision on this service? d. Two weekdays are chosen at random. What is the probability that on both of these days there will be fewer than 23 riders from the subdivision on this service? e. Find the mean and standard deviation of the number of riders from this subdivision on this service on a weekday. f. If the cost of a ride is $\$ 1.50$, find the mean and standard deviation of the total payments of riders from this subdivision on this service on a weekday.
The following table shows the probability distribution of for the discrete random variable X= the number of traffic accidents reported in a day in a small city in the Midwest. x 0 1 2 3 P(x) 0.23 0.17 0.26 0.34 1. The probability of less than 1 accident is: a. 0.23 b. 0.40 c. 0.32 d. 0.60 2. The mean (expected value) of X is: a. 1.17 b. 1.71 c. 0.17 d. 0.71 3. The probability that X will be at least 2 is: a. 0.26 b. 0.34 c. 0.60 d. 0.66
David N.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD