Probability & Statistics Ch.2 Section 1 Question 9

Solutions for “Probability and Statistics: The Science of Uncertainty” (Second Edition). These are solutions I have come up with; I offer no guarantee of accuracy.

Question

Let $S=\{1,2,3,4\}$ , $X=\textit{I}_{\{1,2\}}$ , $Y(s)=s^2 X(s)$ .

a) Compute $Y(1)$ b) Compute $Y(2)$ c) Compute $Y(4)$

Solution

(a) Compute $Y(1)$

Y(1)=1^2 \times X(1) = 1 \times 1 = 1

(b) Compute $Y(2)$

Y(2)=2^2 \times X(2) = 4 \times 1 = 4

(c) Compute $Y(4)$

Y(4)=4^2 \times X(4) = 16 \times 0 = 0