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November 2003 S1 Question

How would you do part a)? The mark scheme has me stumped :/
Nov 2003 question.docx241.5KB
Reply 1
Avatar for raheem94
raheem94
13
Original post by Dirtyflanker
How would you do part a)? The mark scheme has me stumped :/


Its a discrete uniform distribution, so use the formula, E(X)=n+12 E(X) = \dfrac{n+1}2
Reply 2
Avatar for Dirtyflanker
Dirtyflanker
OP
Original post by raheem94
Its a discrete uniform distribution, so use the formula, E(X)=n+12 E(X) = \dfrac{n+1}2


I did that but to get all the marks you have to derive it from the probability distribution :s-smilie:
Reply 3
Avatar for raheem94
raheem94
13
Original post by Dirtyflanker
I did that but to get all the marks you have to derive it from the probability distribution :s-smilie:


E(X)=∑x×P(X=x)=1n+2n+3n+⋯+nn=1n(1+2+3+⋯+n) \displaystyle E(X) = \sum x \times P(X=x) = \frac1n + \frac2n + \frac3n + \cdots + \frac{n}{n} = \frac{1}{n} ( 1 + 2 +3+ \cdots + n)

Use n2(2a+(n−1)d) \displaystyle \frac{n}2(2a+(n-1)d) for (1+2+3+⋯+n) ( 1 + 2 +3+ \cdots + n)

1n(1+2+3+⋯+n)=1n(n2(2+(n−1)1))=1n(n2(n+1))=n+12 \displaystyle \frac{1}{n} ( 1 + 2 +3+ \cdots + n) = \frac{1}{n} \left( \frac{n}2 \left(2 + (n-1)1 \right) \right) = \frac1n \left( \frac{n}2 (n+1) \right) = \frac{n+1}2

Now input the values and find n n
Reply 4
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Dirtyflanker
OP
Wow, thanks :smile: wouldn't have expected the need for that formula in an s1 exam though :s
Reply 5
Avatar for linhx
linhx
help me please..... who knows how to do the probabiltity question q2..
q: a fairground game involves trying to hit a moving target with a gunshot. a round consists of up to 3 shots. ten points are scored if a player hits the target, but the round is over if the player misses. linda has a constant probability of 0.6 of hitting the target and shots are INDEPENDENT OF ONE ANOTHER. (WHAT DOES THIS MEAN, HOW CAN I SHOW IT ON A TREE DIAGRAM OR ISIT A VENN DIAGRAM??)

a) find the probability that linda scores 30 points in a round

The r.v X is the no. of points linda scores in a round.
b) find the probability distribution of X
c) find the mean n SD of X

A game consists of 2 rounds
d)find the probability that linda scores more points in round 2 than in round 1.
(edited 11 years ago)
Reply 6
Avatar for Dirtyflanker
Dirtyflanker
OP
Don't have the answers in front of me, but I sort of remember doing it a while back:
a) P(HHH) = 0.6 x 0.6 x 0.6
b) x 0 10 20 30
P(x)0.4 0.6x0.4 0.6x0.6x0.4 0.6x0.6x0.6

See the tree diagram attached. By independent- it just means that the probability of the next event happening is not dependent on the previous probability ie- a hit is always 0.6 and a miss is always 0.4.

c) Just use the formulas
d) Always write out what the possibilities are, so if she needs more points in round 2 than in round 1 you can write it out as:

Round 2 Round 1
P(10) P(0) Multiply each set together and add up all the probabilities and that's your answer :smile:oug9yfuo.png
P(20) P(0)
P(30) P(0)
P(20) P(10)
P(30) P(10)
P(30) P(20)

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