Probability

Understanding Data

Variance - Properties

         

The probability distribution of a random variable XX is

P(X=1)=0.1P(X=2)=0.2P(X=3)=0.3P(X=4)=0.4.\begin{array}{c}&P(X = 1) = 0.1 &P(X = 2) = 0.2 &P( X = 3) = 0.3 &P( X = 4) = 0.4. \end{array}

If Y=9X+14, Y = 9X+14, what is the variance of Y?Y?

A random variable XX has E(X)=3E(X)=3 and V(X)=9.V(X)=9. If Y=aX+b,E(Y)=6,V(Y)=9,\begin{array}{c}&Y=aX+b, &E(Y)= 6, &V(Y) = 9,\end{array} what are a(>0)a(>0) and b?b?

If V(X)=4 V(X) = 4 , what is V(2X+7)? V(2X + 7 )?

If V(X)=3 V(X) = 3 and E(X2)=10,E(X^2) = 10, what is (E(X))2? (E(X))^2 ?

If V(X)=5 V(X) = 5 , what is V(2X+4)? V(2X + 4 )?

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