Probability and statistics for computer science, all the info is provided in the picture! Please help asap! I will give good ratings :)

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Determine whether the following statements are true or false. Justify your answers with proof if the statement is correct and with an example (contradiction) if the statement is wrong. 0 If E[X] 3 E[Y], then Variance of X is greater than variance of Y. 0 Suppose X ~ N(0,a) and Y ~ N(U,b]. Also, suppose that f is the PMF function of X, and g is the PMF function of Y. If a 2 b, then f(0) 2 9(0). 9 For random variable X, event A happens if X = 1, and event B happens if X = 2. We can say that A and B are independent. 0 Suppose P(A D B) = P(A)P(B], P(A ﬂ 0) = P(A)P(C), P(C 0 B) = P(C]P(B]. Then we can conclude that P(A n B D C} = P(A]P(B]P(C}.

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