AS Maths Statistics Random Variable Problem

dxnixl

Hi,

I’m struggling with the following question. I’ll attach it in the next post. Any helps appreciated

Thxs

Bump
Help plz

Original post by dxnixl

Bump
Help plz

What have you tried / what are you stuck with? You must know binomial formula etc?

Reply 4

dxnixl

Original post by mqb2766

What have you tried / what are you stuck with? You must know binomial formula etc?

Yep I know the binomial formula and substituted r with k, but it’s impossible to simplify.

Reply 5

mqb2766

Original post by dxnixl

Yep I know the binomial formula and substituted r with k, but it’s impossible to simplify.

Which one did you try and looking at the first probability, 0.02, k must be fairly small?
Or use the guassian approximation if you've covered that?
Post your working?

(edited 4 years ago)

Reply 6

dxnixl

Original post by mqb2766

Which one did you try and looking at the first probability, 0.02, k must be fairly small?
Post your working?

I’ve never seen a problem like this so this is all I managed

0B0F21DA-F4D0-4852-9784-C78B4167AAD4.jpeg52.4KB

Reply 7

mqb2766

Original post by dxnixl

I’ve never seen a problem like this so this is all I managed

Is that the same question / answer?

Reply 8

dxnixl

Original post by mqb2766

Is that the same question / answer?

No it’s a similar question but with P(50,0.4) however it’s asking for the same thing. I just want to focus on the question in the original post

Thxs

Reply 9

mqb2766

Original post by dxnixl

No it’s a similar question but with P(50,0.4) however it’s asking for the same thing. I just want to focus on the question in the original post

Thxs

How about putting right numbers in for the question you're asking
What is the value when k=0, k=1 ...? You're being asked to evaulate when the cumulative probability is small, so it must be close to zero?

Reply 10

dxnixl

Original post by mqb2766

I did this... but idk if that’s how the answers correct. It seems like trial and error

Reply 11

RDKGames

Study Forum Helper

Original post by dxnixl

I’ve never seen a problem like this so this is all I managed

Why is

X

distributed binomially under the parameters

n=50,p=0.4

?

Question clearly states

X \sim B(40,0.1)

.

Anyway,

\displaystyle P(X<k) = P(X \leq k-1) = \sum_{r=0}^{k-1} P(X=r) = \sum_{r=0}^{k-1} \binom{40}{r}(0.1)^r(0.9)^{40-r}

You can enter this into your calculator. The only thing you need to vary is the upper limit of the sum. You should try some small values first and see if your result is

<0.02

. If it is, increase the upper limit by 1 and look at the new result.
Keep doing this until you get a probability that is

>0.02

.

The upper limit will be precisely the value of

k

Reply 12

mqb2766

Original post by dxnixl

I did this... but idk if that’s how the answers correct. It seems like trial and error

Right answer, but your answer is really looking the probabilities, not their cumulative value. Same result, but you'd need to be clear in your working

Reply 13

dxnixl

Original post by mqb2766

Right answer, but your answer is really looking the probabilities, not their cumulative value. Same result, but you'd need to be clear in your working

Could you please show a working example for all the questions above?

I don’t mind if you use a different value for p and n, it’d just give a clear idea as to how I should approach the question(s). That way, I can apply it to this and other similar questions

Reply 14

mqb2766

Original post by dxnixl

Pretty much what you've done, but
P(x < k) = P(x=0) + P(x=1) + ... + P(x=k-1)
You've tested the values, not their sum, on the right. You need to test the cumulative sum. Same result though.

(edited 4 years ago)

Reply 15

Notnek

Original post by dxnixl

I did this... but idk if that’s how the answers correct. It seems like trial and error

Trial and error is the best way to do questions like this. Assuming you're using your calculator (if you're not then you should be), you should be using the cumulative binomial function to find P(x<=k).

Reply 16

AGrizzlyBearo

If you haven't already, get yourself an a level calculator:

https://www.amazon.co.uk/FX-991EX-Advanced-Scientific-Calculator-VERSION/dp/B0719FWP3X/ref=mp_s_a_1_2?keywords=a+level+calculator&qid=1581100826&sr=8-2

Reply 17

dxnixl

Original post by mqb2766

Pretty much what you've done, but
P(x < k) = P(x=0) + P(x=1) + ... + P(x=k-1)
You've tested the values, not their sum, on the right. You need to test the cumulative sum. Same result though.

Ahh I think I got it! Ty! If I have an issue I’ll post here! :smile:

same for @Sir Cumference and @RDKGames

Reply 18

dxnixl

Hey, just managed to finish my painful HW! Thankyou :smile:

@RDKGames @AGrizzlyBearo @Sir Cumference @mqb2766

6B3FD9E5-7743-4D3B-9FF4-254136224FB0.jpeg129.9KB

Reply 19

mqb2766

Original post by dxnixl

Hey, just managed to finish my painful HW! Thankyou :smile:

@RDKGames @AGrizzlyBearo @Sir Cumference @mqb2766

Note that a guestimate for Q8 would be the normal approximation (if you've covered this yet)
np = 4
sqrt(npq) ~ 2
So two standard deviations about the mean would give 95% of the mass of the distribution so
0 < X < 8
At around these critical points you'd get the tails of the distribution which is what the question was asking about. Note that the normal approximation is only a guide here ...