Let $X_1$ be an exponential random variable with mean $1$ and $X_2$ be a gamma random variable with mean $2$ and variance $2$. If $X_1$ and $X_2$ are Inde...

For the given : $f(t) = 2sint + \sqrt{3}cost$, we are tasked to find the amplitude, period and phase shift. From the book : $f(t) = 2sint + \sqrt{3}cost$ ...

i know that the values of $\cos n\pi=(-1)^{n}$ and $\sin n\pi=0$. Now i want to know that what is the general expressions of $\cos \frac{n\pi}{2}$ and $\s...

I'm trying to wrap my head around a pretty basic concept. But I'm not 100% sure my reasoning is right. I have an event that happens 10 times, at...

Prove by induction the summation of $\frac1{2^n}$ is greater than or equal to $1+\frac{n}2$. We start with $$1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\...

the equation $ax^2 + bx + c = 0$ has positive roots if $b^2-4ac > 0$ $-b/a > 0$ $c/a > 0$ I would like to know is there any necessary and suffici...

According to C.H. Edwards' Advanced Calculus of Several Variables: The dimension of the subspace $V$ is defined to be the minimal number of vectors r...

In the video game Azur Lane after completing the mission 3-4 you have a chance of getting as a reward one of the two aircraft carriers Akagi and Kaga. The...

I've seen copious usage of prepositions like "on" and "over" in mathematical texts with no concrete description of what they mean. Can someone please...

This is another question like this one. And by the same reason, the book only has the final answer, I'd like to check if my reasoning is right. A cou...