The random variableW takes the values 1.5, 3, 6 and 7 with probabilities0.2, 0.25, 0.4 and 0.15, respectively.

1- Compute the expectation ofW=

2- Compute the expectation ofW^2 =

3- Compute the variance ofW=

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Q2 : Define the cumulative distribution functionF(t) oft byF(t)=P(Wt) . Shade the region consisting of each point(x,y) in whichx0 , andF(X)y1.

Compute the area of the shaded region=