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?
The distribution should be of the Poisson type. There is a certain expected value "a" of an accident occurring during that interval on a given Friday. You can compute it using
a = 0.84*0 + 0.138*1 + 0.02*2 + 0.01*3 a = 0.208
For a = 0.208, the probability of m=0 accidents according to a Poisson distribution is
P(0) = (a^m e^-a)/m! = e^-.208 = 0.812
P(1) = 0.208*0.812/1 = 0.169
P(2) = 0.208^2*0.812/2 = 0.018
P(3) = 0.208^3*0.812/6 = 0.001
These are in pretty good agreement with your numbers, except for the probability of 3 accidents. Did you mean to write 0.001?
you completely lost me when you responded and put 0.138*1 in your reply. May I ask where did you get 0.138?
To graph the probability distribution, we will plot the number of accidents on the x-axis and the corresponding probabilities on the y-axis.
The number of accidents (x) can take on values of 0, 1, 2, or 3. The probabilities (P(x)) associated with each value of x are 0.84, 0.13, 0.02, and 0.01, respectively.
So, the probability distribution will look like this:
x | P(x)
---------------
0 | 0.84
1 | 0.13
2 | 0.02
3 | 0.01
To calculate the expected value for the random variable (E(X)), we will multiply each value of x by its respective probability and sum them up. Mathematically, E(X) = Σ(x * P(x)).
E(X) = (0 * 0.84) + (1 * 0.13) + (2 * 0.02) + (3 * 0.01)
= 0 + 0.13 + 0.04 + 0.03
= 0.2
Therefore, the expected value for the random variable "number of accidents" is 0.2.