a. Answer:The corresponding probabilities are obtained by converting the percentages into probabilities. That is, by dividing each value with 100.
F/N (where F =percentage of accidents and N =100)
Step-by-step explanation:
X 0 1 2 3 4
f(X) 0.096 0.57 0.238 0.077 0.019
b. The formula for the expected value of a discrete random variable is E(x)= µ=∑xf(x)
X F(X) X.f(X)
0 0.096 0
1 0.57 0.57
2 0.238 0.476
3 0.077 0.231
4 0.019 0.076
Total 1 1.353
Hence, the value for expected value of X is 1.353
The formula for the variance of the discrete random variables is Var(x)= σ² =∑(x-µ)²f(x)
X F(X) (x-µ) (x-µ)² (x-µ)².f(x)
0 0.096 -1.353 1.8306 0.1757
1 0.57 -0.353 0.1246 0.0710
2 0.238 0.647 0.4186 0.0996
3 0.077 1.647 2.7126 0.2089
4 0.019 2.647 7.0066 0.1331
Total 1 3.235 12.0930 0.6884
Hence, the variance of the random variable x is 0.6884
The formula for the standard deviation of the discrete random variables is
σ=√(∑[(x-µ)².f(x)] )
Thus, the standard deviation is σ= √0.6884
=0.8297
Hence, the standard deviation of the random variable x is 0.8297