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QUESTION

# 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)