Question

a box contains five ball. the balls are numbered 1,2,3,4 and 5. a person randomly draws to balls from the box. let X be the sum of the numbers kf the ball drawn. what is the sum of all probabilities, P(X=x)?

Answer 1

There are $\dbinom{5}{2}=10$ outcomes.

$$\def\arraystretch{1.5} \begin{array}{c:c} Sample\ point & X \\ \hdashline 1,2 & 3 \\ \hdashline 1,3 & 4 \\ \hdashline 1,4 & 5 \\ \hdashline 1,5 & 6 \\ \hdashline 2,3 & 5 \\ \hdashline 2,4 & 6 \\ \hdashline 2,5 & 7 \\ \hdashline 3,4 & 7 \\ \hdashline 3,5 & 8 \\ \hdashline 4,5 & 9 \\ \hdashline \end{array}$$ $$\def\arraystretch{1.5} \begin{array}{c:c} x & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline p(x) & 0.1& 0.1 & 0.2 & 0.2 & 0.2 & 0.1 & 0.1 \\ \end{array}$$

Check

$$\sum_ip(x_i)=0.1+0.1+0.2+0.2+0.2+0.1+0.1=1$$

$$mean=E(X)=\sum _ix_ip(x_i)=3(0.1)+4(0.1)$$

$$+5(0.2)+6(0.2)+7(0.2)+8(0.1)+9(0.1)=6$$