Question

The only information available to you regarding the probability distribution of a set outcomes is the following list of frequencies:

X 0 15 30 45 60 75
Frequency 25 125 75 175 75 25

(a) construct a probability distribution for the set of outcomes.
(b) Find the expected value of an outcome.

Answer 1

a) $P(X) = \frac{f_i}{N}$

N = 25+125+75+175+75+25=500

b) E(X) = Σ(XP(X))

$= 0 \times 0.05 + 15 \times 0.25 + 30 \times 0.15 + 45 \times 0.35 + 60 \times 0.15 + 75 \times 0.05 \\ = 36.75$