Expected value and variance

Question

Let Y be a random variable with p(y) given in the accompanying table. Find E[Y ],
E[1/Y ], E(Y² -1), V(Y)

y 1 2 3 4
p(y) 0.4 0.3 0.2 0.1

 

I know that V(Y) means the variance but what does E(1/Y) and E(Y² -1) mean ?

Answer 1

These expressions are just fun tions of the random variable.

 

Just calculate the values for these functions respectively as seen below:

 

Y           1     2     3      4

1/Y.        1   1/2  1/3  1/4

Y²-1.      0    3     8      15

 

then proceed as how you calculate expected value.

 

for instance, E(1/Y) = 1*0.4 + (1/2)*(0.3) +( 1/3)*(0.2) + (1/4)*(0.1) =. 13/15