Question: 2. Consider the function F(x) = ? + =(arctan(x) + = ) for -00 ) for oc < a: < oc . 2. Consider the

2. Consider the function F(x) = ? + =(arctan(x) + = ) for -00

) for oc < a: < oc . 2. Consider the function F (x) Is F (x) a c.d.f.? Explain by referring to the properties Of a c.d.f. If a continuous random variable X has cumulative distribution function F Find E(X) and Var(X) and indicate if each of E(X) and Var(X) are finite. Find the p.d.f. Of Y k. (Remember to specify the range Of Y.) find the p.d.f. Find E (Y). Is it true that E(k) Hint: + arctan(:r) = and + (arctan x (r2+1)

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