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The Bernoulli distribution is a distribution whose random variable can only take 0 or 1
- The value of E(x2) is p
- The value of V(x) is p(1 - p)
- The value of E(x79) is p
The distribution is given as:
p(0) = 1 - p
p(1) = p
The expected value of x2, E(x2) is calculated as:
So, we have:
Evaluate the exponents
Multiply
Add
Hence, the value of E(x2) is p
<h3>How to compute V(x)</h3>This is calculated as:
Start by calculating E(x) using:
So, we have:
Recall that:
So, we have:
Factor out p
Hence, the value of V(x) is p(1 - p)
<h3>How to compute E(x79)</h3>The expected value of x79, E(x79) is calculated as:
So, we have:
Evaluate the exponents
Multiply
Add
Hence, the value of E(x79) is p
Read more about probability distribution at: