Freckles and moles on humans are very common. However usually large, abnormally

Question

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

Explanation / Answer

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)

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