Science & Mathematics - 20 November 2007

I have to show that the density of the sum of 2 independent random variables is equal to:
f(x) = 1/(2sqrt(π)) * e^(-x^2/4)

Now I know that the formula needed is:
[-infinity to +infinity]∫f(x)(f(z-x)

And that a random variable X has a normal distribution if it has density:
f(x) = 1/(sqrt(2π)) *e^(-x^2/2)

This is what I’ve done so far:
(1/2 π) ∫ e^(-x^2/2) * e^(-(z-x)^2/2) dx

Now just focusing on the exponents:
(-2x^2 + 2xz)/2 – (z^2/2)
= - (x^2 – xz) – (z^2/2)
= - (x^2 – xz + z^2/4) – z^2/4

So the integral is now:
(1/2 π) * e^(-z^2/4) ∫ e^(-(x-1/2z)^2 dx

I said that the integral can be evaluated by subbing in u = x-1/2z.
du = dx.

So now I’m left with:
∫e^(-u^2) du.

I’m confused by how to get from this expression to 1/(2sqrt(π)) * e^(-x^2/4) because I thought that ∫e^(-u^2) du couldn't be computed.

2007-11-20 10:17:48 · 1 answers · asked by cornz000 1 in Mathematics

This is how far i got:
ORIGINAL EQUATION: 6x+6(4)=3x-2
6x+24=3x-2

2007-11-20 10:17:37 · 5 answers · asked by Sarah B 1 in Mathematics

2007-11-20 10:16:40 · 5 answers · asked by ma.roddy 1 in Mathematics

2007-11-20 10:15:07 · 1 answers · asked by Anonymous in Zoology

In the combustion of 250 g of propane with an excess of hydrogen, what volume of carbon dioxide is produced at 290 K and 1.5 atm. Choose from the following possible answers:

11904.5 L
270 L
90 L
404 L

2007-11-20 10:14:31 · 2 answers · asked by Goddess Allure 2 in Chemistry

2007-11-20 10:12:00 · 3 answers · asked by Jansen J 4 in Astronomy & Space

I have to write a paper and i'm finding to many varying answers.

Which ones are right?

The Sun's rays are more perpendicular in the summer.
The Earth is closer to the Sun in summer.
The Earth's axis is tilted away from the sun in summer.
The Sun is up in the sky for longer in the summer
The Sun has a slight yearly change in the light it emits.

2007-11-20 09:59:22 · 5 answers · asked by Angelical Abby 4 in Astronomy & Space

If you could participate in a hot debate over the need for a new definition of a planet...
What would be the main point you'd argue? Would you be for or against it?, why and why not?, and where is your stance in the controversy it's created surrounding Pluto? Was demoting Pluto...the right decision?, why or not?

(Not asking for an essay, this is part of a research project)

2007-11-20 09:57:09 · 3 answers · asked by Emocide Organ 3 in Astronomy & Space

a.cecum
b.right dorsal colon
c.stomach

2007-11-20 09:57:05 · 3 answers · asked by Anonymous in Zoology

i have a project tom. and i need to know were to go to find the scientific names of leaves?

2007-11-20 09:55:08 · 4 answers · asked by Jennifer G 1 in Botany

For the ions: N3 - , CO3 (2-), NO3 -, and BF4 -
i need to find out how to find the structures and central atom hybridizations. I am not focusing well right now as I am trying to recover from a virus and all of this is looking Greek to me right now....HELP!

2007-11-20 09:54:20 · 2 answers · asked by Anonymous in Chemistry

Show proof and explain your answer (not to graphic...gross)

2007-11-20 09:54:11 · 5 answers · asked by ss 2 in Astronomy & Space

1: Two jets leave an airport at the same time in opposite directions. The first jet is traveling at three hundred forty one mph and the other at three hundred thirty two mph. How long will it take for the jets to be 1,616 miles apart?

d r t
jet 1
jet 2


673 minutes
2.4 hours
2 hours 40 minutes
2 hours

2007-11-20 09:52:58 · 9 answers · asked by Est.1992 6 in Mathematics

2007-11-20 09:51:47 · 27 answers · asked by Anonymous in Biology

2007-11-20 09:51:20 · 5 answers · asked by Alexander 6 in Physics

1.) A regular triangular pyramid with a slant height of 9m has a volume equal to 50 m^3. Find the lateral area.
the answer must be 84.65m^2

2.) A liquid vessel which is initially empty is in the form of an inverted regular hexagonal pyramid of altitude of 25ft and base edge 10 ft. How much surface will rise if 6779 liters of water is added?
the answer must be 12 ft.

please help me with these problems...

2007-11-20 09:50:06 · 1 answers · asked by greeK_god_HirYu 3 in Mathematics

than normal. A physical examination reveals that he has normal temperature, pulse and respiration and is maintaining his regular weight. The dog is eting normally. Which one of the following would be the next diagnostic step to assess his health status?

a. bladder radiographs
b. urinalysis
c. cardiac ultrasound

2007-11-20 09:45:16 · 6 answers · asked by Anonymous in Zoology

Describe in your own words the differences between the probability of an event and the relative frequency

2007-11-20 09:41:59 · 3 answers · asked by Anonymous in Mathematics

2007-11-20 09:41:20 · 2 answers · asked by Ayomide B 1 in Biology

i got the first derivative is
y'=(3x^2)/(2y)
Then i think you do quotient rule on the right side, but what do you do on the left?

2007-11-20 09:36:50 · 7 answers · asked by Tim H 1 in Mathematics

And would this have na effect on the Earth's orbit?

2007-11-20 09:36:43 · 12 answers · asked by peaches & love 1 in Astronomy & Space

calculate the volume of SO2(g) produced when 2.00 liters of o2 react with excess sulfer at constant temperature and pressure.

2007-11-20 09:27:31 · 2 answers · asked by confusedkid 3 in Chemistry

sec 4x = 2

tan 3x = 1

2007-11-20 09:23:23 · 2 answers · asked by Anonymous in Mathematics

Which of the following statements are true for the reaction


Ca(OH)2(aq) + HCl(aq) →



a) CaCl(aq) is a product

b) When balanced the coefficient of HCl(aq) is 3

c) Only ions appear in the net ionic equation

d) Ca(OH)2(aq) appears in the net ionic equation

e) H2O(l) appears in the net ionic equation

2007-11-20 09:22:33 · 2 answers · asked by sovietwarhawk 1 in Chemistry

Can you find numbers less than 200 that is divisible by four different prime numbers why or why not? Answer really descriptively and plz don't joke around answer as soon as possible it is due on 11/21/07

2007-11-20 09:18:29 · 5 answers · asked by Anonymous Girl 2 in Mathematics

2007-11-20 09:14:02 · 6 answers · asked by Anonymous in Mathematics

I need to make a poster about reconnaissance satellites. The problem is, there isn't much declassified information about them because they're mostly classified by the government. I was hoping someone could help me out. On the poster I need to include: general weight and size, structure, what instruments these satellites use, their primary user, specific tasks of reconnaissance satellites, their type of orbit and typical orbital path and height, and other related information, like their history, development, and future. Thank You !!!

2007-11-20 09:08:35 · 6 answers · asked by pjp 1 in Astronomy & Space

I have found one way which is A=39 B=41 C=43 D=44 E=47 but my teacher asked us to Verify our answer wich means i need another answer. Please help

2007-11-20 09:07:45 · 1 answers · asked by tigard344816 1 in Mathematics

If yes, then how would this affect their research?

If no, tell me HOW we KNOW that they are not emotionally attached to their theories.

2007-11-20 09:07:37 · 8 answers · asked by Jack 5 in Biology

2007-11-20 09:04:47 · 13 answers · asked by Tee tee 1 in Weather