Want to make sure i understand. The order of rolls doesn't matter. They are pairwise independent. However, not mutually independent be because P (R_j,k , R_a,b) is 1/6^3 and P (R_j,k) is 1/6 with district indices j,k,a,b
Homework Statement
Roll a fair die 5 times, find the probability that the first two rolls have the same outcomes.
Homework Equations
The Attempt at a Solution
The total outcomes is 6^5, I think we have 6^2 * 6 choose 2 /6^5 since the first two numbers are fixed and we can choose 2 numbers...
Homework Statement
Let Y_1,Y_2 be independent random variable with uniform distribution on the interval [1,2]. Define X=max{Y_1,Y_2}. Find p.d.f., expected value and variance.
Homework Equations
The Attempt at a Solution
Since $X=\max\{Y_1,Y_2\}$, this tells $Y_1$ and $Y_2$ must at most $x$...
Homework Statement
It rains in a city with a chance of 0.4. The weather forecast is not always accurate. When there will be a rain the next day, the forecast predicts the rain with probability 0.8; When there is no rain, the forecast falsely predicts a rain with probability 0.1. You take your...
Hi, all. I am planning to apply REU for math this summer. This is my first time to write a personal statement, I am not sure how it is. Basically, my statement needs to answer why I want to apply this program and what my future goal is.
Malcolm X said: “Education is our passport to the future...
Homework Statement
Let F = {0,1,α,α+1}. Find all irreducible polynomials over F of degree at most 2.
Homework Equations
The Attempt at a Solution
To determine an irreducible polynomial over F, I think it is sufficient to check the polynomial whether has a root(s) in F,
So far, I got...
Homework Statement
If the function f:ℝ→ℝ is differentiable and f(x)<=f(0) for all x ∈[-1,1], then f'(0)=0. True or False.
Homework Equations
The Attempt at a Solution
I think the statement is right. Since f(x)<= f(0) for all x in [-1,1], this tells us f is an even function or a symmetric...
Homework Statement
A one to one function f: ℝ→ℝ is monotone, True or False
Homework Equations
The Attempt at a Solution
I think the statement is false, for example: Let I =[0,1]∪[2,3] f(x)=x if x∈[0,1], f(x)=5-x,x∈[2,3]
Homework Statement
The state of Oregon wishes to design a new lottery game with the following rules: 1.Each ticket costs $5 2.There will be three prizes: $10, $100 and $1000 3.The probability of the $10 prize will be 20%. 4.The probability of the $100 prize will be 1% 5.Ten thousand...
I am getting confusing about the question, the investment increased 0.4 in 3 years, and in this 3 years increasing by the same rate, that is how I understand the question.
the investment is increasing at the same rate in 3 years, and we are looking for the rate,r. In order to get the value after 3 years which is already increase 40%, I think (1+r)^3 is the rate increase over 4 years. Thus, this would equal to 1+0.4