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Is there more information available? There is no answer without knowing f(x). Maybe as an exercise try various functions.

So it is not clear what (2), how it is parameterise. However what you are looking for is the mode. If you search hypergeometric distribution on wikipedia it should have page with statistics on distribution such mean, mode etc. I was not able to find proof of the theorem with a quick search...

geometric distribution

This appears multinomial distribution. The fraction containing the factorials is essentially the number of permutations extremely similar to the binomial distribution

So if take a look at the proof that should give you insight. There is chain of inequalities in proof 1. You should find integral of xf(x) from x to infinity there.

The theorem mention is very similar to Markov's Inequality, however the integral on the right-hand-side has a lower-bound of x instead of zero. I think it might be interesting to see if the theorem is actually true so maybe test some probability density function on it such as exponential or...

I think I understood the content. The text seems a little bit off with the wording. Instead of saying joint distribution function for definition 11 they should say joint cumulative distribution function. https://en.wikipedia.org/wiki/Cumulative_distribution_function So what they really want...

Give the question a go first so we can see what you have tried

P(X>x) is just some number between 0, 1 integral_from_0_to_infinity P(X>x) - P(X<-x) dx If X belongs to a pdf where the domain is the positive set of real numbers this will mean and x>0 P(X>x) > 0, P(X<-x) = 0. P(X>x) = 1 - cdf(x) Maybe this could help give you an idea. Maybe next...

You have not written a question. What are your definition, axiom, theorems? Are you referring to any textbook? If so have you tried using Quizlet in conjunction to a disposable email. temp mail etc

It looks like you might have swapped the definitions of a, b. Have another look. The triangle that was drawn in the image is not correct, your image. This because the the size of angle corresponds the length the side. So since 90 degrees is largest angle the side opposite the angle i.e...

It should be a - b = 100

The unit circle definition of sin is, sin theta = y, So sin theta is positive in the first and second quadrants. So it is impossible to get an negative answer if you are using degrees. I don't see way to use solve this question without using sine rule.

Assuming you have followed the working out of Jimmysmith the negative answer it is most likely due to your calculator being in radians. You will need switch the mode of the calculator from radians to degrees. To do this you should be able to find a manual online for your calculator you could use...

For part a) we are assuming the maximum displacement is 4? Do you have the answer for part a) For b ii) you need just find the smallest value of t such that x= -2 and t >0.

Have you run into any trouble with partial fractions? - I guess when reverse chain rule is possible or you think a u-substitution might work - When the degree of the numerator is greater than the degree in the denominator # maybe you might use partial fractions later on after long division

Also I don't understand what the question is trying to ask? So the question is telling you to construct a differential equation that can model the amount salt in the tank per time t. A differential equation is equation involving some rate of change or in other words derivative. Generally for...

Use an online integral calculator with full steps. My guess is let u = 1+x

Is it in the textbook? Or if you want you could check the website with the syllabus such as NESA.

What is RCR