The number of accidents that occur at the intersection of Pine and Linden streets between 3 p.m. 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?
0.84*0 + 0.12*1 + 0.02*2 + 0.01*3 = 0.19
is the expected number of accidents (on average).
To graph the probability distribution, you can create a bar graph where the horizontal axis represents the number of accidents (0, 1, 2, 3), and the vertical axis represents the probability associated with each number.
Here is how you can calculate the expected value for the random variable:
1. Multiply each number of accidents by its corresponding probability.
- For 0 accidents: 0 * 0.84 = 0
- For 1 accident: 1 * 0.13 = 0.13
- For 2 accidents: 2 * 0.02 = 0.04
- For 3 accidents: 3 * 0.01 = 0.03
2. Sum up all the products:
0 + 0.13 + 0.04 + 0.03 = 0.2
The expected value for the random variable, in this case, is 0.2.
Based on the probabilities provided, the graph for the probability distribution of the number of accidents at the intersection of Pine and Linden streets between 3 p.m. and 6 p.m. on Friday afternoons would look like this:
```
Accidents | Probability
0 | 0.84
1 | 0.13
2 | 0.02
3 | 0.01
```
The expected value represents, on average, the number of accidents you would expect to occur at the intersection during that time frame based on the given probabilities. In this case, the expected value is 0.2, suggesting that, on average, you would expect to see approximately 0.2 accidents at the intersection between 3 p.m. and 6 p.m. on Friday afternoons.