Question

If X is the random variable model ‘the number on a biased die’, and the probability distribution function of X is as shown below,

Answer 1

As here the question is incomplete, so suggested the solution based on the given terms.

Given,

Random variable on biased die = X

p(x) = P(X=x) for all the value of x

Now, the variance of a random variable X

$\Rightarrow V(X)= E[(X-\mu)^2]$

For the case of the die toss,

Expected values $E(X)=\Sigma_{x\in X}(xP(x))$

Now, for the calculation of variance,

$E(X^2)=\Sigma x^2 P(x)$

$Var(X)=E(X^2)-E^2(X)$