The following table shows part of the probability distribution for a random variablex.

x f(x)

0 0.2

1 ?

2 0.15

3 ?

4 0.3

(a)The mean of the above distribution is known to be2.15(i.e.,E(x) =2.15).

Determinef(1)andf(3).

f(1)=____________

f(3)=____________

(b) Compute the variance and the standard deviation for the above probability distribution. (Round your standard deviation to three decimal places.)

variance=_____________

standard deviation=_______________