ku

Toss a die twice and take the sums. Let A be the event that the sum of the two numbers rolled is 6. Let B be the event that you roll a 6 on the first roll. Is there a negative relationship between A and B? I believe there is, but I'd like to have my working checked out. $AB = \emptyset$ and therefore $P(AB)=0$. $A = \{(1,5), (2,4), (3,3), (4,2), (1,5)\}$ and therefore $P(A)=\frac{5}{36}$ $B = \{(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)\}$ and therefore $P(B)=\frac{6}{36}=\frac{1}{6}$ $P(AB) < P(A)P(B)$ $\frac{P(AB)}{P(B)}=P(A)$ $P(A|B) < P(A)$

A creationist once told me that the probability that evolution occured according to scientific theory is very low. There is a low probability that the steps of naturalistic processes that occur could happen that way. But I've been thinking. If you take a coin and flip it a billion times, whatever result you get, the probability of obtaining that result is extremely low, yet is that evidence that what you just did (flip the coin a billion times) didn't occur?

I forgot to add that $U(x,y)=xy$. It's very easy now. All that needs to be done is to show that RHS=LHS.

$x=\frac{m}{2p_{x}}$ and $x^{h}=\sqrt{u\frac{p_{y}}{p_{x}}}$. How do I show that $\frac{\partial{x}}{\partial{p_{x}}}=\frac{\partial{x^{h}}}{\partial{p_{x}}}-\frac{\partial{x}}{\partial{m}}x$?

Since economics is a science, what do you think about an economics forum?

I heard somewhere that when two brothers are born, the younger one's peak height is nearly always greater than the older one's. Why does the younger sibling have this advantage? What is the biological or genetic explanation?

A coin is tossed until a head occurs and the number of tosses required is observed. What is the sample space? The answer is $\Omega = \{1,2,3,...\}$ and my lecturer said, "one, two, three, till infinite." But if you flip a coin inifite times, wouldn't you expect heads to come up half the time...?

$U = f(x,y)$ Can someone explain to me how $\frac{dy}{dx}=-\frac{\partial{U}/\partial{x}}{\partial{U}/\partial{y}}$? _______________ http://members.fortunecity.com/ku20/oldindex.html

Is there a method researchers can use to measure a person's degree of satisfaction? What hormones or chemicals are measured if we wanted to guage a person's happiness? Or do we measure brain activity? What area of the brain is asociated with happiness or satisfaction? If it were possible to do such research, media executives can more accurately predict how much satisfactions viewers will get from movies, books, newspapers, etc.

When we do not sleep, we feel miserable. Science knows now that this miserable feeling is a defence mechanism because sleeping is important in organizing thoughts, which is important for survival. In a similar way, group pride--the force that makes religion and nationalism very popular--could be an instinct preserved through evolution because individuals who ally with others increase fitness.

If you're studying creative writing in the Arts department, they only require you to write a summary of the novel and then write out the most important parts.

Could pride (e.g. pride of one's achievements or pride of one's country) be an evolutionary defense mechanism designed to reward organisms to (1) engage in productive activity that aids survival (for individual achievement) and (2) form allies with others (group pride, like pride for country)?

Is is unhealthy for a 9-year-old boy to bodybuild? For example, if a 9-year-old started weightlifting and strenously exercising in an attempt to make himself bigger.

I have an optical mouse, not a ball mouse. My dad told me that optical mouses work best on white surfaces, but from usage I find that red surfaces work best. Does it matter what is the color of the surface on which you use your optical mouse?

If you consitently stay up late (say sleep at 4 am) and wake up late (say 12 noon), is this bad for you? You are still getting 8 hours of sleep per day. The only problem I can think of with this sleeping habit is that you tend to be up when there is no sunlight and this may lead to vitamin D deficiencies...but this is probably minor and you can probably compensate for vitamin D deficiencies by drinking more milk.

If a food is in a plastic container and I heat up the food while it is in the plastic container, does the melted plastic contaminate the food? What about with plastic wrapping?

After reading http://www.ananova.com/news/story/sm_365484.html I was just wondering whether it would be possible to create a pill that could make someone's skin paler. Theoretically would it be possible? http://members.fortunecity.com/ku20/oldindex.html