Variance - Definition

         

What is the variance of the following probability distribution: P(X=1)=0.5,P(X=0)=0.2,P(X=1)=0.3?\begin{array}{c}&P(X = -1) = 0.5, &P(X = 0) = 0.2, &P( X = 1) = 0.3 ?\end{array}

When all values of a dataset are doubled, what happens to the variance?

You throw a coin twice. The prize is 5050 dollars if it lands heads, and 44 dollars if it is tails. If XX is the total prize you will end up receiving, then what is the variance of X?X ?

The probability distribution of a random variable XX is P(X=1)=a,P(X=2)=b,P(X=3)=0.4.\begin{array}{c}&P(X = 1) = a, &P(X = 2) = b, &P( X = 3) = 0.4. \end{array} If ab=0.05a \cdot b=0.05 and ab,a \geq b, then what is the variance of X?X?

The probability distribution of a random variable XX is P(X=1)=0.1,P(X=2)=0.2,P(X=3)=a.\begin{array}{c}&P(X = 1) = 0.1, &P(X = 2) = 0.2, &P( X = 3) = a.\end{array} What is the variance of X?X?

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