Homework SourseFreckles and moles on humans are very common However usually
Freckles and moles on humans are very common. However usually large, abnormally shaped and/or abnormally colored freckles/moles can sometimes be warning signs of skin cancer.
Let X be the number of “unusual” freckles/moles found on patients that are seen by a dermatologist’s office in Bloomington. We’ll assume that an individual can only have between 0 and 4 unusual moles/freckles each, hence X = {0,.....,4}. The population probability distribution for the number of unusual freckles/moles is presented in the following table.
0.05
(a) Find P(X 2).
(b) Find P(X > 1).
(c) Find P[X < 2 or X 3].
(d) Find X.
(e) Find x^2
What i need is part E only.
| X | 0 | 1 | 2 | 3 | 4 |
| p(x) | 0.4 | 0.3 | 0.15 | 0.10 | 0.05 |
Solution
Consider the table:
As
sigma^2(x) = E(x^2) - E(x)^2 = 2.6 - 1.1^2 = 1.39 [ANSWER]
| x | P(x) | x P(x) | x^2 P(x) |
| 0 | 0.4 | 0 | 0 |
| 1 | 0.3 | 0.3 | 0.3 |
| 2 | 0.15 | 0.3 | 0.6 |
| 3 | 0.1 | 0.3 | 0.9 |
| 4 | 0.05 | 0.2 | 0.8 |
| Totals | 1.1 | 2.6 | |
| =E(x) | =E(x^2) |
