Last Minute Questions

[Asx4Life]

If we are asked to find the median and we are given a table
x              0      1      2      3      4
Pr(X=x)   0.1   0.2   0.2   0.4   0.1
The Median is 2.5 right? Can someone explain to me why?

 

[abeybaby]

say you ran this thing 10 times. you would get:

0 1 1 2 2 3 3 3 3 4

the median of which is 2.5. so this leads to the theory:

You sum the probability from left to right. The x value for which you pass 0.5 is the median. If you land exactly on 0.5, then you average that x value and the next one.

[Asx4Life]

Thanks!

Also, a question is worth 2 marks and its like find the deriavative for f(x)=e^2x(sin(3x))
Is it sufficient to just write
f(x)=e^2x(sin(3x))
f'(x)=2e^2x(sin(3x))+3e^2x(cos(3x)) to obtain 2 marks

or do I need to shows the chain rule like let u=e^2x and v=sin(3x)
and go like f'(x)=uv'+vu' then solve?


And stricly increasing/decreasing functions.
eg: y=x^2  given X E (-2,2]
What values is the function strictly increasing/decreasing? Do we include endpoints with closed or open brackets?

[abeybaby]

its enough to get you full marks, unless its a show that question. for a show that question, you'd have to say, by product rule etc etc...

so f is strictly increasing over [x1,x2] if a>b implies that f(a)>f(b) for any a,b in [x1,x2].

so for that one, strictly increasing when x E [0,2] and strictly decreasing when x E (-2,0]

[Asx4Life]

Thanks
I need help with this one too
Show that the graph of h(x) = x^n/e^x
, where n is a positive integer,
has a local maximum at x = n.

[abeybaby]

omg i just did that!!!!!!!!!
fine i'll type it... 1 sec

[abeybaby]

here you go!

[Asx4Life]

here you go!

Thanks, took me awhile to understand the last lines though

[abeybaby]

fair enough, thats where the actual work is though...