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S2 CRV question help!!

Hi!!!
So, one of the questions on my homework looks like this:

and I got a = -26.4 and b = 39/55

Just wanted to know if this is right because they're weird numbers lol thanks :biggrin:

Reply 1

Kevin De Bruyne

Original post by ltbitters

Hi!!!
So, one of the questions on my homework looks like this:

and I got a = -26.4 and b = 39/55

Just wanted to know if this is right because they're weird numbers lol thanks :biggrin:

One way to check is to integrate f(x) between 1 and 0 and seeing if it is equal to 1. As F(1) = 1.

(edited 7 years ago)

Reply 2

ltbitters

Original post by SeanFM

One way to check is to integrate f(x) between 1 and 0 and seeing if it is equal to 1. As F(1) - F(0) should equal 1.

oh nooo

it doesnt equal zero and idk what i did wrong D:
i tried creating simultaneous equations with E(X) and integrating to equal 1 rip

Reply 3

Kevin De Bruyne

Original post by ltbitters

oh nooo

it doesnt equal zero and idk what i did wrong D:
i tried creating simultaneous equations with E(X) and integrating to equal 1 rip

It should equal 1 but I think that's a typo.

Also, f(x) can't be negative so your -26.4 is a bit of a red flag :tongue:

but no worries

What were your simultaneous equations? :h:

Reply 4

ltbitters

Original post by SeanFM

It should equal 1 but I think that's a typo.

Also, f(x) can't be negative so your -26.4 is a bit of a red flag :tongue:

but no worries

What were your simultaneous equations? :h:

ahhh yep it didnt equal 1 either tho so lol :lol:

I had no idea f(x) couldn't be negative though so thanks for the tip there :biggrin:

I had 0.6 = a(1/4 b - 1/5) and 1 = a(1/3 b - 1/4) and then multiplied them both so they equalled 6

Reply 5

Kevin De Bruyne

Original post by ltbitters

ahhh yep it didnt equal 1 either tho so lol :lol:

I had no idea f(x) couldn't be negative though so thanks for the tip there :biggrin:

I had 0.6 = a(1/4 b - 1/5) and 1 = a(1/3 b - 1/4) and then multiplied them both so they equalled 6

Yeah, f(x) is the probability of whatever it is being x, so if it's negative.. then you have a negative probability :hide:

How did you get those questions though? I'm sure you solved them correctly but maybe they aren't the right ones to use..

Given that the mean is 600 (how can you find the mean in terms of a and b, using properties of a CRV?) and F(upper limit, in this case 1) where F is the CDF is equal to 1.. you should be able to get 2 equations.

Reply 6

ltbitters

hoo boy i think i found what i did wrong lmaooo i divided 10 by 6 and got 0.6 :lol:

Reply 7

ltbitters

Original post by SeanFM

Yeah, f(x) is the probability of whatever it is being x, so if it's negative.. then you have a negative probability :hide:

ohh i didnt use a cdf :0
i just set E(X) to 0.6 (x is in the thousands or litres and the mean is 600 litres) and then integrated x.(abx^2-ax^3) between 1 and 0 for the first equation and integrated abx^2-ax^3 between 1 and 0 and set it equal to 1 for the second??

im not sure if my equations are right tbh but i found the most stupid mistake in my working (10/6 = 0.6 apparently) and now my answers are a=12 and b=1 which seem like a lot nicer numbers lmao

Reply 8

Kevin De Bruyne

Original post by ltbitters

Ah good, your method to get the equations were right then :smile:

You can use your integrated step as well to find F(1) (substituting in a and b) and then you'll be able to check :tongue:

Reply 9

ltbitters

Original post by SeanFM

Ah good, your method to get the equations were right then :smile:

You can use your integrated step as well to find F(1) (substituting in a and b) and then you'll be able to check :tongue:

awesome !! i think i might have this now :biggrin:

tytyty so much for the help lol sorry for wasting time w/ a stupid mistake tho :lol:

Reply 10

Kevin De Bruyne

Original post by ltbitters

awesome !! i think i might have this now :biggrin:

tytyty so much for the help lol sorry for wasting time w/ a stupid mistake tho :lol:

No problem at all :h:

if you can, with questions spot if you can self-validate the answer in any way using what you know.. (for simultaneous equations in general, see if the solutions satisfy one or both equations for example) or use CDFs/PDFs etc..