Thread: 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

can you explain the answers as well please

B
can you explain the

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) ....

can you explain the answers as well please

B
can you explain the

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