Question

For two independent random variable x
and y, E(X)=3, E(y)=2, V(X)= 1.2, V(y)=1.
Then what is the value of V(3x-2y) ? *
(1 Point)
6.8
12
14.8
13​

Answer 1

Answer:

13 is the correct answer

Answer 2

✪ᴀɴsᴡᴇʀ✪

• $Var(3x - 2y) = 14.8$

᯽ғᴏʀᴍᴜʟᴀ᯽

If X and Y are independent RVs, then

• $E[aX±bY] = aE[X] ±bE[Y]$

• $Var(aX±bY) = a^2 Var(X) + b^2 Var(Y)$

★ᴄᴀʟᴄᴜʟᴀᴛɪᴏɴ★

Using above formula,

$Var(3X - 2Y)$

$=3^2Var(X) + 2^2 Var(Y)$

$=9\times 1.2 + 4\times 1$

$=10.8 + 4$

$=14.8$