For every claim write if it is true or false. Write a short explanation. (a) The

Question

For every claim write if it is true or false. Write a short explanation.

(a) The sum of two continuous random variables is a continuous random variable.

(b) Let X, Y be random variables. Then Var[X + Y ] = Var[X] + Var[Y ].

(c) Let X, Y, Z be random variables, then E[X + Y |Z] = E[X|Z] + E[Y |Z].

(d) Let Xi exp(1) be independent and An = {Xn > log(n)}, then P[lim sup An] = 1 if and only if 2.

(e) Let X, Y N (µ, 2 ) be independent random variables, then P[X > Y ] doesn’t depend on µ and 2 .

Explanation / Answer

1] True

Sum of two continuous random variables is continuous random variable

2)] FALSE

Equality holds only when x & y are independent

3)]TRue

Equality holds.

4)] true

Statement is true

5] True

Given probability independent of u & s2

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