Homework Statement
I need to answer a bunch of topological questions based on the cartesian product of two sets, but I'm not entirely sure how to graph them out.
I have A = [1,2)U{3} and B = {1, (1/2), (1/3), ...}U[-2,-1). S = A x B, and I need the graph of S.
Could anyone help me with...
Given that a random variable X follows an Exponential Distribution with paramater β, how would you prove the memoryless property?
That is, that P(X ≤ a + b|X > a) = P(X ≤ b)
The only step I can really think of doing is rewriting the left side as [P((X ≤ a + b) ^ (X > a))]/P(X > a). Where...
I'm doing a practice problem for my upcoming midterm and am stuck on a question.
3. The number of hurricanes that occur in the caribbean during hurricane season is a random variable, where the mean number of hurricanes occurring is 8, or E(X) = 8, with a standard deviation of 2.83.
(a) Find...
Having a lot of trouble with this question.
So first I tried making an equation, and I wrote that the probability = P(rolling a 6)+P(rolling a 6 and not a 7 on the first roll and not a 9 on the first roll) + P(rolling a 6 and not a 7 on the first roll and not a 9 on the first roll and not a 7...
Homework Statement
Find the unique solution to the differential equation
y''+4y'−5y=−435sin(2t)
satisfying the initial conditions y(0)=29 and y'(0)=47
The Attempt at a Solution
So (I think) I found the correct general solution. I let y(t)=Acos(2t)+Bsin(2t) and eventually worked...
Homework Statement
Find the particular solution of the differential equation y''+36y=0 satisfying the conditions y(0)=−4 and y(pi/12)=3.
Your answer should be a function of x.
The Attempt at a Solution
I think I know how to do this kind of question, and I can't see where I'm going...