Edexcel Mathematics S2 26th June 2017 - Unofficial Mark Scheme

3a) E(X) was 22.5 because it was in 'tens of hours'. Missed by many, will only cost 1 mark if you left it as 2.25

Think you need to square your answer to 3c as you needed both batteries to still be working for the radio to be working, and i'm pretty sure 6e was 11/24

Pretty sure it just asked for E(x) which is 2.25. Because the variable is in tens of hours itself, that's what X is measuring, so you shouldn't times by 10, you're working something else out by doing that.

Hmmm, you may be right. It did also say "by integration" so I can kind of imply that the value you get when using the integration is the value you use... who knows? I'll edit my post again.

2) b) 5 minutes (That's the most common answer on the discussion thread - if somebody could write a decent concise method, I'll be glad to edit it in)

3) c) P(X>2.5)/P(X>1/6) = 125/256 (This answer might need squaring, as it is to do with 2 batteries: this would result in 0.2384)

6) e) I got F(5.5) - F(4) as E(X) was 4, by symmetry. This got me 0.7583, but as someone pointed out, it has to be less than 0.5. Their answer was 0.4, while someone else got 11/24.

3a) E(X) was 22.5 because it was in 'tens of hours'. Missed by many, will only cost 1 mark if you left it as 2.25

Method:
X ~ Po(2.5t/60), where t is the number of minutes
P(X = 0) = 1 - 0.2
e^-(2.5t/60) = 0.8
-2.5t/60 = ln0.8
t = -60/2.5 * ln0.8 = 5.355
so to the nearest minute the answer is 5.
[Note:]

A lot of people mistakenly got 38 from using ln0.2 - this can be shown to be wrong by common sense. The average rate was 2.5 calls per hour, which is one call every 24 minutes. So the probability that there are no calls in 38 minutes would definitely be more than 20% (in fact, it's 80%).

I'm sure the two batteries bit was the previous part, and I got 125/256 so I think that's correct.

My answer was 11/24. Note that P(X < E(X)) = 0.5 by definition, so you don't need to calculate E(X). F(5.5) = 23/24 and 23/24 - 1/2 = 11/24.

It's a good point but while we're being pedantic, E(X) = 2.25 is correct; the mean is 22.5 hours but the expected value of the statistic is 9/4. Since the question asked for E(X), I can't imagine people will lose marks for this; but conversely, getting a value of 2.25 and then saying "so mean battery life is 22.5 hours" is also perfectly fine.

I really messed up this paper😭 it's so hard to remember with stats what i got and my calculator only goes back a few values, just hoping i've got over 70 UMS, any ideas how many marks that would be?

I'm sure the two batteries bit was the previous part, and I got 125/256 so I think that's correct.
Note that P(X < E(X)) = 0.5 by definition

Method:
X ~ Po(2.5t/60), where t is the number of minutes
P(X = 0) = 1 - 0.2
e^-(2.5t/60) = 0.8
-2.5t/60 = ln0.8
t = -60/2.5 * ln0.8 = 5.355
so to the nearest minute the answer is 5.
[Note:]

A lot of people mistakenly got 38 from using ln0.2 - this can be shown to be wrong by common sense. The average rate was 2.5 calls per hour, which is one call every 24 minutes. So the probability that there are no calls in 38 minutes would definitely be more than 20% (in fact, it's 80%).

I'm sure the two batteries bit was the previous part, and I got 125/256 so I think that's correct.

My answer was 11/24. Note that P(X < E(X)) = 0.5 by definition, so you don't need to calculate E(X). F(5.5) = 23/24 and 23/24 - 1/2 = 11/24.

It's a good point but while we're being pedantic, E(X) = 2.25 is correct; the mean is 22.5 hours but the expected value of the statistic is 9/4. Since the question asked for E(X), I can't imagine people will lose marks for this; but conversely, getting a value of 2.25 and then saying "so mean battery life is 22.5 hours" is also perfectly fine.

Its entirely possible I misread the question, so maybe idk
Isn't that the definition of the median, it only works in this case as its symmetrical

Its entirely possible I misread the question, so maybe idk
Isn't that the definition of the median not E(X), it only works in this case as its symmetrical