Recent content by Tomp

Kinda urgent help! Probability function - E(2^X)?? Question A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t) Find the pmf of X My solution x f(x) 1 0.3 2 0.4 3 0.6 5 0.1 The next question asks Calculate E(2^X) Which I am totally...

Question An expert sharpshooter misses a target 10 percent of the time. I have a question "What is the probability that the fi rst miss comes after the 3rd shot?" Is this as simple as 0.9^3 * 0.1?

Question A moment-generating function of X is given by M(t) = 0.3e^t + 0.4e^(2t) + 0.2e^(3t) + 0.1e^(5t) Find the pmf of X My attempt x f(x) 1 0.3 2 0.4 3 0.2 4 0 5 0.1 I am just wondering whether it is correct to say "0" for 4 or is it more correct to say x f(x) 1 0.3 2 0.4 3 0.2 5 0.1 or...

Thanks for your detailed response. My tutor hasn't been incredibly clear about what he means by a "nutural language proof", but based on the examples provided by my lecturer, they indicate the idea of a very compressed proof (in steps) where he assumes the axioms. For these reasons, I...

Would I have to indtroduce something like (there exists) w such that x + w = 0 So, 1. x + y = 0 premis 2. ∃w x + w = 0 3. x + y + w = w commutative axiom 4. y + 0 = w 5. y = w 6. x + z = 0 premis 7. z = w 8. (y = w) ^ (z = w) --> x = z transivity axiom therefore (x + y = 0) ^ (x + z = 0) → (y...

I have been given a question by my tutor to try out for our next class Using the axioms for addition of numbers give a natural language proof that the additive inverse of a number is unique, that is prove: ∀x∀y∀z (x + y = 0) ^ (x + z = 0) → (y = z) I am new at writing proofs! My...

My lecturer posted a question asking why ""Real Analysis is all about infinity" Why is this so?

That there exists a x0 between (r1,r2) such that f'(x0) = 0

I understand what you are saying. This is all that was given in the question and now I am stumped!

This doesn't necessarily need to be true, f(a) can just equal f(b), but i assumed that they equaled zero as it's asling about the roots

f must be continuous between two roots [a,b] and also differentiable on (a,b)...f(a)=f(b)=0 (roots) there exists c in (a,b) such that f'(c) = 0 ...

I'm doing a question and I am getting stuck and need help. I am not sure where to start or how to do a proof for this question. We have not done a question like this in class before. Homework Statement Question: Consider the continuous functions f(x) = 1 - e^(x)*sin(x) and g(x) = 1 +...

I'm doing a question and I am getting stuck and need help Question: Consider the continuous functions f(x) = 1 - e^(x)*sin(x) and g(x) = 1 + e^(x)*cos(x). Using Rolle's Theorem, prove that between any two roots of f there exists at least one root of g. Hint Remember that, a root of f is a...

I am trying to complete a previous exam and have come across a question which I am unable to do. I know how to complete an epsilon delta proof for limits, however, not to prove continuity... We haven't seemed to cover this in our lecture notes :/ Using an epsilon-delta technique, prove that...

Homework Statement Using only the fi eld axioms, prove that if x,y ε R and x = y then wx = wy. Homework Equations http://mathworld.wolfram.com/FieldAxioms.html The Attempt at a Solution The solution to this can be solved within 2 lines or so using the field axiom...