What is theoretical mean, variance of random var uniformly dist on (0,1) ?

Cleverdiva

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Nov 9, 2017
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1. What is the theoretical mean and the theoretical variance of a random variable,uniformly distributed in the interval (0,1)?

2. If Xi, Xj are real-valued random variables with zero mean and variance of one,what will be the mean value and the variance of the complex random variableY=Xi+jXj?
 
So, for Number 1 I came up with this:

f(x) = 1, 0≤ x ≤ 1 and 0, otherwise

Mean E(X) = Integral of x f(x) from 0 to 1
= 0.5

Variance V(X) = E(X^2) - [E(X)]^2

= Integral of x^2 f(x) - (Mean)^2
= 1/3 - 1/4
= 1/12

Is this right?
 
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