Suppose X is a discrete random variable and k is a constant. If E(3X+k)=26 and E(2k-X)=3 , what is E(X)?

1 Answer
Jan 29, 2016

#E(X)=7#

Explanation:

The calculation is nearly similar to substitution equation except for this time, you used density function as its equation.

For a discrete random variable #X#, where #a# and #b# are constant, the equation is given as;

#E [ a X +- b ] = a E(X) +- b#

So, in order to find #E(X)# you need to rearrange the equations, which can be seen as;

#E(3X+k)=26#
#3E(X)+k=26# ----- #(1)#

#E(2k-X)=3#
#-E(X)+2k=3# ----- #(2)#

Then, to solve for #E(X)#, we can use substitution equation;

From #(1)#;
#3E(X)+k=26#
#k=26-3E(X)# ----- #(3)#

Substitute #(3)# into #(2)#;
#-E(X)+2k=3#
#-E(X)+2(26-3E(X))=3#
#-E(X)-6E(X)=3-52#
#-7E(X)=-49#
#E(X)=7#