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3 years ago

9

FIND THE AREA The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round to th

e nearest tenth.

1 answer:

qwelly [4]3 years ago

5 0

There is no picture, so i cannot help

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Let X and Y be independent continuous random variables that are uniformly distributed on (0,1). Let H=(X+2)Y. Find the probabili

belka [17]

Looks like there are two distinct problems here.

"Let X and Y be independent ..."

$P(\ln H\ge z)=P(\ln((X+2)Y)\ge z)=P((X+2)Y\ge e^z)=P\left(Y\ge\dfrac{e^z}{X+2}\right)$

Conditioning on $X$ involves interpreting this probability for all possible fixed values of $X=x$ :

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=\displaystyle\int_xP\left(Y\ge\dfrac{e^z}{X+2}\text{ and }X=x\right)$

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=\displaystyle\int_xP\left(Y\ge\dfrac{e^z}{X+2}\mid X=x\right)P(X=x)$

We have $x\in(0,1)$ , and over this domain $P(X=x)=1$ . Since $X=x$ is fixed, we can omit the conditioning notation to leave us with

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=\displaystyle\int_0^1P\left(Y\ge\dfrac{e^z}{x+2}\right)\,\mathrm dx$

$Y$ has CDF

$P(Y\le y)=F_Y(y)=\begin{cases}0&\text{for }y1\end{cases}$

Then we can write our integral as

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=\displaystyle\int_0^1\left(1-F_Y\left(\frac{e^z}{x+2}\right)\right)\,\mathrm dx$

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=\displaystyle\int_0^1\left(1-\frac{e^z}{x+2}\right)\,\mathrm dx$

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=x-e^z\ln(x+2)\bigg|_{x=0}^{x=1}$

$P\left(Y\ge\dfrac{e^z}{X+2}\right)=\boxed{1-e^z(\ln2-\ln3)}$

"Let X be a standard normal ..."

Using the method of distribution functions, we have

$F_Z(z)=P(Z\le z)=P(F_X(X)\le z)=P(X\le {F_X}^{-1}(z))=F_X({F_X}^{-1}(z))=z$

$\implies\boxed{f_Z(z)=\begin{cases}1&\text{for }z\in(0,1)\\0&\text{otherwise}\end{cases}}$

4 0

2 years ago

Simple Interest and Compound Interest.<br>Guys I need help with this question.

kotegsom [21]

Answer:

Simple interest at 2.1%

Step-by-step explanation:

If you had $200 to start

Simple would be $200 x 2.1% = $4.2

$4.2x3 years = $12.60

Total money after 3 years $212.60

Compound would be $200 x 2.7% = $5.40 1st year

$205.40 x 1.4% = $2.8756 (2.88 rounded) 2nd year

$208.28 x 1.4% = $2.9159 (2.92 rounded) 3rd year

3 years total = $211.20

$212.60 greater then $211.20

5 0

3 years ago

425,339,253 what’s the rule

mixer [17]

The rule is subtracting 86 each time

3 0

3 years ago

PLEASE HELP ME!!!

Ksju [112]

Answer:

: )

Step-by-step explanation:

Create a graph and plug in the information you can use desmos or look up other work time check in sites its much easier

4 0

3 years ago

there are 30 students in mr. Holland music class. If 30% of the students play in the school band, how many students in the class

Bond [772]

To calculate percentage, we turn the percentage into a decimal.

30% of 30 = 0.3 of 30 = 0.3 x 10

0.3 x 10 = 3

3 students play in the school band.

7 0

3 years ago