What is the value of this integral February 12    3

Suppose that $f(z)=1/(b-a) , a≤z≤b$, and $f(z)=0$ , otherwise.Now, I want to find the following integral: $$g(x,y)=\int_{-\infty} ^\infty f(x-z)f(y-z)dz$$I would appreciate if you could help me. Thanks.Note that $$\int_\mathbb R\mathbf 1_{x-b\lt z\lt

Probability of Type II error February 12

I have these values:A sample of size 100 100 is taken from the population.Standard Deviation is 5Mean 125H0: $ \mu=$ 125 against Ha:$ \mu<125 $ Accept H0 if the sample mean $\bar{\mathbb{x}} $ is ≥ 124Reject H0 if the sample mean $\bar{\mathbb{x}} $

What type of discontinuity is found in this graph February 12

What type of discontinuity is found in this graph
$f(x)$ = 1/$x$ when $x$ > 0 $f(x)$ = 4 when $x$ < 0What type of discontinuity is present when $f(x)$ = 0

Modeling integers in NLP February 12

I was wondering why it is not OK to model binary (integer) variables of an optimization problem, in the following formx(x-1) = 0 What are the consequences for an NLP (solved with IP)? Isn't it better to avoid converting an NLP problem to an MINLP? Wh

Probability that the sum of 50 dice throws is $\geq 195$ February 12    4

The question is: A cyclist is going for a bike journey of $1950$ kilometres. Every morning he tosses a die, and if the outcome is $k$, where $k = 1, 2,\dots,6$, he cycles $10k$ kilometres on that day. Find the probability that he will finish his rout

Solving polynomial equation modulo $p^n$ February 12    1

I have to solve the equation $$ X^4 - 3 X^2 + 27 \equiv 0 \bmod 5^k$$ for the first few $k = 1, \ldots, 6$I don't even know how to start, ok, for $k=1$ $$ X^4 - 3 X^2 + 27 \equiv 0 \bmod 5\, ,$$ I can guess an answer, like $X \equiv 4 \bmod{5}$, but

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