Browse Questions

# A discrete random variable X has the probability distribution given as below:

X 0.5 1 1.5 2 P(X) k $k^2$ $2k^2$ k \begin{array}{1 1}(i)\quad Find\;the\;value\;of\;k \$ii)\quad Determine\;the\;mean\;of\;the\;distribution\end{array} Can you answer this question? ## 1 Answer 0 votes Toolbox: • X-random variable • X={\(0.5\;1\;1.5\;2$}
• $\sum^4_{\substack{I=1 }} P(X_I)$
• Mean=$X_1P(x_1)$+$X_2P(X_2)$+$X_3P(X_3)$+$X_4P(X_4)$
$p(x_1)$=K$p(x_2)=K^2\ p(x_3)=2K^2 p(x_3)$=K
$K+K^2+2K^2+K=1$
$2K+3K^2=1$
$3K^2+2K-1=0$
$3R(K+1)-1(K+1)=0$
$(3K-1)(K+1)=0$
3K-1=0
3K=1
K=$\Large\frac{1}{3}$
$X_1$=$.5$$X_2$=1$X_3$=1.5$X_4$=2
$mean=\Large\;\frac{1}{3}\;\times\;.5\;+\;(\frac{1}{3})^2 +2(\frac{1}{3})^2\times1.5+\frac{1}{3}\times2$
=$\Large\frac{1}{6}$+$\Large\frac{1}{9}$+$\Large\frac{1}{3}$+$\Large\frac{2}{3}$
=$\Large\frac{23}{18}$

edited Jun 4, 2013