E3. SupposeX1 is the number of Heads in 5 tosses of a fair coin, and X2

is the number of Tails inthe same 5 tosses. Which of the following

statements are true, and which false?

(a) X1 and X2 are independent

(b) E(X1 + X2)= 5

(c) X1 + X2 = 5

(d) Var(X1 )= Var(X2 )

(e) The correlation between X1 and X2 is -1

(f) E(X1X2 )= E(X1 )(fX2 )

(g) Taken individually, X1 and X2 have the same distribution

(h) Var(X1 + X2 )= 0

can you explain the answers as well please

B

can you explain the