1. The probability distribution of Y, the number of imperfections per 10 meters of a synthetic fabric in continuous rolls of uniform width is given by
|
yi
|
0
|
1
|
2
|
3
|
4
|
|
f(yi)
|
0.41
|
0.37
|
0.16
|
0.05
|
0.01
|
| |
|
|
|
|
|
a. Find the probability that the number of imperfections for the fabric is less than 2.
b. Give the cumulative distribution for 2? y < 3.
c. Calculate the expected value for this distribution.
d. Calculate the variance and standard deviation for this distribution.