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?
To graph the probability distribution, you need to plot the probabilities for each possible outcome.
Let the random variable X represent 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.
The possible values of X are 0, 1, 2, and 3, with corresponding probabilities of 0.84, 0.13, 0.02, and 0.01, respectively.
To graph this probability distribution, you can create a bar chart where the x-axis represents the number of accidents (0, 1, 2, 3), and the y-axis represents the probabilities.
Here is the graph of the probability distribution:
```
Number of Accidents (X) | Probability
------------------------|-----------
0 | 0.84
1 | 0.13
2 | 0.02
3 | 0.01
```
To find the expected value for the random variable given the number of accidents, you need to multiply each possible value by its probability and sum them up.
Expected Value (μ) = (0 × 0.84) + (1 × 0.13) + (2 × 0.02) + (3 × 0.01)
= 0 + 0.13 + 0.04 + 0.03
= 0.20
Therefore, the expected value for the random variable (number of accidents) is 0.20.