SOLVEEEE NOWWWWW HURRRYYYYYY

Suppose that W1, W2, and W3 are independent uniform random variables with the following distributions: Wi ~ Uni(0,10*i). What is

nadya68 [22]

I'll leave the computation via R to you. The $W_i$ are distributed uniformly on the intervals $[0,10i]$ , so that

$f_{W_i}(w)=\begin{cases}\dfrac1{10i}&\text{for }0\le w\le10i\\\\0&\text{otherwise}\end{cases}$

each with mean/expectation

$E[W_i]=\displaystyle\int_{-\infty}^\infty wf_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac w{10i}\,\mathrm dw=5i$

and variance

$\mathrm{Var}[W_i]=E[(W_i-E[W_i])^2]=E[{W_i}^2]-E[W_i]^2$

We have

$E[{W_i}^2]=\displaystyle\int_{-\infty}^\infty w^2f_{W_i}(w)\,\mathrm dw=\int_0^{10i}\frac{w^2}{10i}\,\mathrm dw=\frac{100i^2}3$

so that

$\mathrm{Var}[W_i]=\dfrac{25i^2}3$

Now,

$E[W_1+W_2+W_3]=E[W_1]+E[W_2]+E[W_3]=5+10+15=30$

and

$\mathrm{Var}[W_1+W_2+W_3]=E\left[\big((W_1+W_2+W_3)-E[W_1+W_2+W_3]\big)^2\right]$

$\mathrm{Var}[W_1+W_2+W_3]=E[(W_1+W_2+W_3)^2]-E[W_1+W_2+W_3]^2$

We have

$(W_1+W_2+W_3)^2={W_1}^2+{W_2}^2+{W_3}^2+2(W_1W_2+W_1W_3+W_2W_3)$

$E[(W_1+W_2+W_3)^2]$

$=E[{W_1}^2]+E[{W_2}^2]+E[{W_3}^2]+2(E[W_1]E[W_2]+E[W_1]E[W_3]+E[W_2]E[W_3])$

because $W_i$ and $W_j$ are independent when $i\neq j$ , and so

$E[(W_1+W_2+W_3)^2]=\dfrac{100}3+\dfrac{400}3+300+2(50+75+150)=\dfrac{3050}3$

giving a variance of

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{3050}3-30^2=\dfrac{350}3$

and so the standard deviation is $\sqrt{\dfrac{350}3}\approx\boxed{116.67}$

# # #

A faster way, assuming you know the variance of a linear combination of independent random variables, is to compute

$\mathrm{Var}[W_1+W_2+W_3]$

$=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]+2(\mathrm{Cov}[W_1,W_2]+\mathrm{Cov}[W_1,W_3]+\mathrm{Cov}[W_2,W_3])$

and since the $W_i$ are independent, each covariance is 0. Then

$\mathrm{Var}[W_1+W_2+W_3]=\mathrm{Var}[W_1]+\mathrm{Var}[W_2]+\mathrm{Var}[W_3]$

$\mathrm{Var}[W_1+W_2+W_3]=\dfrac{25}3+\dfrac{100}3+75=\dfrac{350}3$

and take the square root to get the standard deviation.

8 0

2 years ago

Consider the situation where 12 people at a picnic want to select an activity for the afternoon. Which activity would win a plur

tatyana61 [14]

Answer is soccer because it has more numbers in the picture

4 0

2 years ago

4 13/20 as a decimal in long devision Form

const2013 [10]

Answer:

4.65

0.65 is 13/20 in decimal form add that to 4 you get 4.65. I don't know what you mean by Long division form since it's just solving in the way of the picture shown up above. But that's not the same equation as this one btw. If you ment something else let me know. Click on it to get full view.

Hope this helps!! If so please mark brainliest and rate/heart to help my account if it did!

6 0

3 years ago

To complete bookshelves, a customer at your store needs to purchase vertical brackets to attach to the wall. The customer wants

stiks02 [169]

We are given with
height = 9 feet
length = 10 feet
wall brackets:
48-in costing $12.95
60-in costing $16.95
distance of brackets from ends = 1 foot
maximum distance between brackets= 24 inches

The brackets are
48/12 = 4 feet
and
60/12 = 5 feet

One of each must be used to cover the height of the shelf

The length of the shelf is
60 inch
subtracting 1 in from each side for the allowance
60 - 2 = 58 in
Dividing by 24 inches
58/24 = 2.41 ~ 3

The total cost is
($12.95 + $16.95) * 3 = $89.7
The total cost of the brackets is $89.7

8 0

2 years ago

Help please 120 50 30 150

Tom [10]

Answer:

Angle 4 will also be 150 degrees

5 0

2 years ago