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

Question

2. 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 (2/X)

X 0 1 2 3 4 p(x) 0.4 0.3 0.15 0.10

0.05

Explanation / Answer

a)

P(x<=2) = P(0) + P(1) + P(2) = 0.4+0.3+0.15= 0.85 [answer]

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b)

P(x>1) = P(2) + P(3) + P(4) = 0.15+0.10+0.05 = 0.30 [answer]

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c)

P(x<2 or x>=3) = P(not 2) = 1 - P(2) = 1 - 0.15 = 0.85 [answer]

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For d and e, consider the table:

Thus,

uX = E(x) = 1.1 [answer, part d]

Do you mean part e mean sigma^2(x) or variance(x)? If so:

Var(x) = E(x^2) - E(x)^2 = 1.39 [answer, part e)

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If part e means something else, please submit it as a separate question. That way we can continue helping you! Thanks!

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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