1. ## prob

E3. Suppose
X1 is the number of Heads in 5 tosses of a fair coin, and X2

is the number of Tails in
the 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

B
can you explain the

2. Originally Posted by hello123
E3. Suppose
X1 is the number of Heads in 5 tosses of a fair coin, and X2

is the number of Tails in
the same 5 tosses. Which of the following
statements are true, and which false?
(a)

X1 and X2 are independent Mr F says: X1 + X2 = 5 so what do you think ....?
(b)

E(X1 + X2)= 5 Mr F says: X1 + X2 = 5 so what do you think ....?
(c)

X1 + X2 = 5 Mr F says: X1 + X2 = 5 so what do you think ....?
(d)

Var(X1 )= Var(X2 ) Mr F says: Refer to your answer to (g). So what do you think ....?
(e) The correlation between X1 and X2 is -1 Mr F says: X1 + X2 = 5 so what do you think ....?
(f)

E(X1X2 )= E(X1 )(fX2 ) Mr F says: True only if X1 and X2 are independent .... So what do yuo think ....?
(g) Taken individually, X1 and X2 have the same distribution Mr F says: Have you thought abut the distribution that each follow?
(h)

Var(X1 + X2 )= 0 Mr F says: See your answer to (d) ....

B
can you explain the

You need to show a bit more effort here. What are your thoughts? Where do you get stuck?