# 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} ## 1 Answer 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