The number of accidents that occur at the intersection of Pine and Linden streets between 3 pm. and 6 pm. on Friday afternoons is 0,1,2, or 3, with probabilities of 0.84, 0.13. 0.02, and 0.01. What is the expected value for the random variable given the number of accidents?

The expected value is sum of n*P(n), for all possible values of n.

0*0.84 + 1*0.13 + 2*0.02 + 3*0.01
= 0.20

To find the expected value (also known as the mean) for a random variable given the probabilities, we need to multiply each possible outcome by its corresponding probability and then add them all together.

In this case, the random variable represents the number of accidents at the intersection of Pine and Linden streets between 3 pm and 6 pm on Friday afternoons. We have four possible outcomes: 0 accidents, 1 accident, 2 accidents, and 3 accidents. The probabilities for each outcome are 0.84, 0.13, 0.02, and 0.01, respectively.

To calculate the expected value, you can use the following formula:

Expected value = (outcome 1 * probability 1) + (outcome 2 * probability 2) + ... + (outcome n * probability n)

Using the given probabilities and outcomes, we can calculate the expected value as follows:

Expected value = (0 * 0.84) + (1 * 0.13) + (2 * 0.02) + (3 * 0.01)
Expected value = 0 + 0.13 + 0.04 + 0.03
Expected value = 0.20

Therefore, the expected value for the random variable representing the number of accidents at the intersection of Pine and Linden streets between 3 pm and 6 pm on Friday afternoons is 0.20.