Var[2X + 3Y] = 2² Var[X] + 2 Cov[X, Y] + 3² Var[Y]
but since X and Y are given to be independent, the covariance term vanishes and you're left with
Var[2X + 3Y] = 4 Var[X] + 9 Var[Y]
X follows an exponential distribution with parameter <em>λ</em> = 1/6, so its mean is 1/<em>λ</em> = 6 and its variance is 1/<em>λ</em>² = 36.
Y is uniformly distributed over [<em>a</em>, <em>b</em>] = [4, 10], so its mean is (<em>a</em> + <em>b</em>)/2 = 7 and its variance is (<em>b</em> - <em>a</em>)²/12 = 3.
So you have
Var[2X + 3Y] = 4 × 36 + 9 × 3 = 171
Answer
8
Step-by-step explanation:
5+12=17 and 17-9=8
Answer:
$0.38
Step-by-step explanation:
First we need to convert pounds to ounces
1 pound = 16 ounces
Thus 16 ounces cost $3
If a portion requires two ounces of butter, we must find out the cost of these 2 ounces, knowing that 16 ounces cost $ 3
ounces cost
16 -- $3
2 -- x
To find the cost x:
![x=\frac{3*2}{16}=$0.375](https://tex.z-dn.net/?f=x%3D%5Cfrac%7B3%2A2%7D%7B16%7D%3D%240.375)
rounding to the nearest cent: $0.38
Your answer would be 5,290
Answer: He and his friends spent 82 hours of watching movies.
Step-by-step explanation: