Suppose that X is a discrete random variable with probability mass function p(x) = cx^2; x = 1; 2; 3; 4: (a) Find the value of c: (b) Find E(X)?

##c = 10/3##

##E(x) = sum x* P(x)##

Properties of p.d.f. include ##sump(x) = 1##

##sum P(x) = 1 ##

=> ## c[1 +4 + 9 + 16 ] = 1 ##

=> ##30c = 1 ##

=>## c = 1/30.E(x) ##

## = (1/30) [1 . 1^2 + 2. 2^2 + 3. 3^2 + 4. 4^2 ] ##

##= (1/30)[ 1 + 8 + 27 + 64] ##

##= 100/30 ##

##= 10/3 ##

##E(x) = sum x* P(x)##