The number of accidents that occur at the intersection of Pine and Linden streets between 3 p.p and 6 p.m. on Friday afternoons is 0, 1, 2, or 3, with probabilities of 0.84, 0.13, 0.02, and 0.01, respectively. Graph this probability distribution. What is the expected value for the random variable given the number of accidents?
To graph the given probability distribution, we can create a bar graph. Each accident count (0, 1, 2, 3) will be represented on the x-axis, and the corresponding probabilities (0.84, 0.13, 0.02, 0.01) will be represented on the y-axis.
Here's how you can create the bar graph:
1. Start by drawing a horizontal line as the x-axis and a vertical line as the y-axis. Label the x-axis as "Number of Accidents" and the y-axis as "Probability."
2. On the x-axis, mark the values 0, 1, 2, and 3 as the accident counts.
3. On the y-axis, mark the probabilities 0.84, 0.13, 0.02, and 0.01 at the corresponding heights.
4. For each accident count on the x-axis, draw a bar that extends upwards to the corresponding probability on the y-axis. The height of each bar should represent the probability.
By following these steps, you will create a bar graph representing the given probability distribution.
Now let's move on to calculating the expected value for the random variable, i.e., the mean number of accidents.
The expected value, denoted as E(X), is calculated by multiplying each possible outcome by its respective probability and summing those products.
For this probability distribution, the expected value can be calculated as:
E(X) = (0 * 0.84) + (1 * 0.13) + (2 * 0.02) + (3 * 0.01)
Simplifying this expression:
E(X) = 0 + 0.13 + 0.04 + 0.03
E(X) = 0.13 + 0.07
E(X) = 0.20
Therefore, the expected value for the random variable (number of accidents) is 0.20.