Let A, B be independent events with P(A) = 0.3, P(B) = 0.7. We define XIA,...

 

Transcribed Image Text:

Let A, B be independent events with P(A) = 0.3, P(B) = 0.7. We define XIA, Y IB and = S: X+Y = (a) (2 Points) Find the set V of possible values of S as well as the prob- abilities P(S = v) that S attains a value v V. (b) (2 Points) Draw the distribution function of S. (c) (3 Points) Show that E(X2) 0.3 = E(Y2)= 0.7 E(XY) = 0.21 = E(X)E(Y). Also find the variance of X and Y. E(X), E(Y), (d) (2 Points) Calculate the expectation E(S) and variance V(S) of S and show that in this specific example we have V(S) = V(X) + V(Y). Let A, B be independent events with P(A) = 0.3, P(B) = 0.7. We define XIA, Y IB and = S: X+Y = (a) (2 Points) Find the set V of possible values of S as well as the prob- abilities P(S = v) that S attains a value v V. (b) (2 Points) Draw the distribution function of S. (c) (3 Points) Show that E(X2) 0.3 = E(Y2)= 0.7 E(XY) = 0.21 = E(X)E(Y). Also find the variance of X and Y. E(X), E(Y), (d) (2 Points) Calculate the expectation E(S) and variance V(S) of S and show that in this specific example we have V(S) = V(X) + V(Y).