Suppose X is a random variable with distribution given be th

Suppose X is a random variable with distribution given be the table What is the expected value of X? What is the variance of X? What is the variance of X?

Solution

E(X)=expected value= sum of all x*f(x)

=0*(1/3) +1*(1/6) +2*(1/3)+4*(1/6)

=1.5

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E(X^2)=sum of all x^2*f(x)

=0*(1/3) +1*(1/6) +2^2*(1/3)+4^2*(1/6)

=4.166667

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

=4.166667 -1.5^2

=1.916667