A commuter must pass through five traffic lights on her way...

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below. $$\begin{array}{l|c|c|c|c|c|c}\chi=\# \text { of Red } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline P(X=x) & 0.05 & 0.25 & 0.35 & 0.15 & 0.15 & 0.05\end{array}$$ a) How many red lights should she expect to hit each day? b) What's the standard deviation?

A commuter must pass through five traffic lights on her way to work and will have to stop at each one that is red. She estimates the probability model for the number of red lights she hits, as shown below.
$$\begin{array}{l|c|c|c|c|c|c}\chi=\# \text { of Red } & 0 & 1 & 2 & 3 & 4 & 5 \\\hline P(X=x) & 0.05 & 0.25 & 0.35 & 0.15 & 0.15 & 0.05\end{array}$$
a) How many red lights should she expect to hit each day?
b) What's the standard deviation?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Discrete Probability Distribution

A discrete probability distribution assigns a probability to each possible value of a discrete random variable. It is used to model scenarios where outcomes are countable, such as the number of events happening in a fixed period or sequence. Understanding the distribution helps in calculating probabilities, mean, variance, and other aspects of the random variable.

Expected Value

The expected value is the long-run average or mean of a random variable, computed as the sum of the products of each value and its corresponding probability. It provides a central measure around which outcomes are expected to cluster, thus serving as a key indicator in decision making and probabilistic modeling.

Variance and Standard Deviation

Variance measures the spread or dispersion of the probability distribution, representing the average of the squared differences from the expected value. The standard deviation is the square root of the variance, providing a measure of dispersion in the same units as the random variable. These metrics help in understanding the degree of variability or risk associated with the outcomes.

Transcript

Please give Ace some feedback