According to the discrete distribution given, the standard deviation is of: 0.98.
The expected value of a discrete distribution is given by the sum of each outcome multiplied by it's respective probability, hence:
[tex]E(X) = 0.1296(0) + 0.3456(1) + 0.3456(2) + 0.1536(3) + 0.0256(4) = 1.6[/tex]
The standard deviation is the square root of the sum of the multiplication of each probability and the difference squared between the observation and the mean, hence:
[tex]\sqrt{V(X)} = \sqrt{0.1296(0-1.6)^2 + \cdots + 0.1536(3-1.6)^2 + 0.0256(4-1.6)^2} = 0.98[/tex]
The standard deviation is of 0.98.
A similar problem is given at https://brainly.com/question/25650097
