Q24 of 108 Page 271

Consider the probability distribution of a random variable X:


Calculate (i) (ii) Variance of X.

We have



Var(X)=E(X2)-[E(X)]2


Where,


And


∴0+0.25+0.6+0.6+0.60= 2.05


And E(X)2=0+0.25+1.2+1.8+2.40=5.65


(i)


As we know Var(ax) = a2 var(x)







(ii) V(X)


Var(X)=E(X2)-[E(X)]2


= 5.65 – (2.05)2


= 5.65 - 4.2025


= 1.4475


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