(Solved): The following table shows part of the probability distribution for a random variable \( x \). (a) ...

The following table shows part of the probability distribution for a random variable \( x \). (a) The mean of the above distribution is known to be \( 2.05 \) (i.e., \( E(x)=2.05) \). Determine \( f(1) \) and \( f(3) \). \( f(1)= \) \( f(3)= \) (b) Compute the variance and the standard deviation for the above probability distribution. (Round your standard deviation to three decimal places.) variance standard deviation