The Official Math/Physics/Whatever Homework questions thread

[Banzai-]

Originally Posted by checktheriver

The computation is correct, P(A|B^c)=1/2.

However, what we are really interested in is P(A|Bg) (and P(A|Cg) ), where Bg is the event "the guard tells him B will be set free" (resp. Cg for C).

Notice that these events are not the same : Bg is always a subset of B^c (same for C), but you cannot have both Bg=B^c and Cg=C^c, because on the intersection of B^c and C^c (i.e. A), the guard must choose between saying B or C.

The probabilities P(A|Bg) and P(A|Cg) will depend on the guard's "strategy", i.e. what he says when both B and C will be set free.
For instance, you can try to show that :
- if he picks 50% B or C, then P(A|Bg)=P(A|Cg)=1/3,
- if he picks B, then P(A|Bg)=1/2 and P(A|Cg)=0.

My answer was writtin thinking they were the same, B^c was the event "the guard tells him B will be set free". Its been a while since ive done anything to do with sets and Id forgotten that ^c was common notation for complements.

Also I should have been clearer that I was assuming the guard's "strategy" was to show no preference to picking B or C. Perhaps this was unjustified, but it seemed trivially obvious that a guard with a bias giving you information is going to affect the probability of your own execution.

[slipstream]

Originally Posted by WAtR

Here is the problem:

This sounds a lot like my favorite variant of the Monty Hall problem, which has the same setup as usual with the one caveat that Monty forgot to take his medication and can't remember which door has the prize behind it. So you pick Door A. In desperation, he flips Door B to reveal... nothing! Mopping sweat from his brow, he then asks whether or not you'd like to switch. Should you?

It's kind of fun to pose this question to people who have just grasped the solution to the original version of the problem. They never get it right.

[Borg7]

f : X → Y is injective if and only if, given any functions g, h : U → X, whenever f ∘ g = f ∘ h, then g = h

Again, I need to prove the above. I've been looking for a few hours now w/o success
Someone please help me out.

[Dasq1306]

Isn't that just an extended definition ?

[Subfallen]

Should be in homework thread?

⇒ Fix g,h: U → X. Suppose that for some u ∈ U, we have f(g(u)) = f(h(u)). Because f is injective, g(u) = h(u). In particular, if f(g(u)) = f(h(u)) for all u ∈ U, then g ≡ h.

⇐ Suppose f(x₁) = f(x₂) for x₁, x₂ ∈ X. We now define two functions g,h: U → X.

For all u ∈ U, g(u) = x₁.
For all u ∈ U, h(u) = x₂.

Thus f(g(u)) = f(h(u)) for all all u ∈ U. By assumption, this requires g ≡ h; which means x₁ = x₂. This proves f is injective.

[lastcardcharlie]

Originally Posted by Dasq1306

Isn't that just an extended definition ?

It's the categorical definition of an injective morphism (no points/elements involved, just other morphisms).

[Borg7]

Great, thanks for the responses

[AceofSpades]

really not quite a homework problem but...

I'm in engineering and taking cal II, doing ok in the class, but I feel like any of the conceptual advanced applied questions I don't have a good sense of how to relate/put it into a mathematical formulation.

any tips on how to make it relevant? or how to learn to better apply it to problem solving?

[Acemanhattan]

Can someone remind me how to factor this kind of trinomial ?

x^2-xy-30y^2

[Tartufo]

Originally Posted by lastcardcharlie

It's the categorical definition of an injective morphism (no points/elements involved, just other morphisms).

More precisely, of a monomorphism. In Sets, these would be the injective functions. (Injective has a different meaning in other settings; in particular it refers to having an extension property w.r.t. monomorphisms.)

[Wyman]

Originally Posted by Acemanhattan

Can someone remind me how to factor this kind of trinomial ?

x^2-xy-30y^2

same idea as factoring a quadratic in one variable.

how do you factor x^2 - x - 30?

[Acemanhattan]

Originally Posted by Wyman

same idea as factoring a quadratic in one variable.

how do you factor x^2 - x - 30?

(x-6) (x+5) i believe


I see now. Thanks

[justfoldpleaseok]

Expected Value question:

The normal weekly demand of a certain perishable product sold by AHOLE Inc is given by the following distribution:
Demand Probability
8 0.1
9 0.2
10 0.1
11 0.4
12 0.2

The product cost AHOLE $5 each. the product sells for $11 each. if not sold by the end of the week, the leftover units must be scrapped.
The supplier only has 10 or 11 units available for AHOLE to purchase. how many would you recomend AHOLE to purchase based on expected profit? (10 or 11)

What is the maximum expected profit?

Im stuck because if AHOLE can only purchase 10 items, does that factor the demand of 11 and 12 out of the question? if so, would this effect the probability of the other (8 9 10) demand since these would be eliminated? can anyone try and lead me into the right direction? THanks for your help

[coffee_monster]

If the demand were 11, but AHOLE only had 10 units, how many would they sell? How much profit or revenue would they get. If the demand were 12?

Now, if AHOLE had 11 units, ...

[justfoldpleaseok]

Originally Posted by coffee_monster

If the demand were 11, but AHOLE only had 10 units, how many would they sell? How much profit or revenue would they get. If the demand were 12?

Now, if AHOLE had 11 units, ...

im lost, sorry i dont follow?