Mean of any probability distribution is given by Mean = ∑x_ip_i

Standard Deviation is given by SD = √Variance where variance is given by:

Variance = ∑ x_i²p_i – (∑x_ip_i)²

∴ first we need to find the products i.e. p_ix_i and p_ix_i² and add them to get mean and apply the above formula to get the variance.

Following table gives the required products :

∴ mean = 0.4+0.6+0.6+0.4 = 2.0

And variance = 0.4 +1.2 + 1.8 + 1.6– (2)² = 1.0

∴ Standard deviation = √1 = 1