Mathematics: Post your doubts here!

Alice123

Alice123

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Dug said:
i)
If the two chosen values are the same, Y takes the value 0. If they are not the same, then Y = Larger X - Smaller X.

Hence, the possible values Y can take are 0, 2 and 4.

Now to draw the table, we need the probabilities.

P(Y = 0) = P(X = 2 and 2) + P(X = 4 and 4) + P(X = 6 and 6)
= (0.5)² + (0.4)² + (0.1)²
= 0.42

P(Y = 4) = P(X = 2 and 6) + P(X = 6 and 2)
= (0.5)(0.1) + (0.1)(0.5)
= 0.1

P(Y = 2) = 1 - P(Y = 0) - P(Y = 4)
= 0.48

ii)
E(Y) = 2(0.48) + 4(0.1) = 1.36
Click to expand...
thanks a lot
 
Dug

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Alice123 said:
https://www.xtremepapers.com/community/members/dug.23386/
please help me with no 6ii? is there any shortcut method? thanks in advance
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w12_ms_62.pdf
Click to expand...
I assume you have used the following method.
3 : 111
4 : 112, 121, 211
5 : 113, 131, 311, 122, 212, 221
6 : 123, 132, 312, 213, 231, 321, 114, 141, 411, 222

You can make it shorter by using permutation.

3 : 3!/3! = 1
4 : 3!/2! = 3
5 : 3!/2! + 3!/2! = 6
6 : 3!/2! + 3!/2! + 3!/2! + 3!/3! = 10

This can be done by intuition alone. I just showed you the working to make you understand. Hope you got it!!
 
syed1995

syed1995

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Alice123 said:
can u pls solve it?
Click to expand...

The method i use is very simple.

Just remember two things.

Ex = mean * n
E(number) = number * n

where n is the total number of people or frequency.

n = 24
E(x-36)=-60
Ex-E36=-60
Ex=-60+E36
Ex=-60+(24*36)
Ex=804

E(x-36)^2 = 227.76
E(x^2-72x+1296) = 227.26 (We just opened the square via the (a-b)^2 = a^2 -2ab + b^2
Ex^2-72Ex+E1296 = 227.26
Ex^2=227.76+72(Ex) - E1296
Ex^2=227.76+72(804) - 24*1296
Ex^2=27011.76 or 27000 (3sf)
 
salvatore

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Kumkum said:
okay, i'll try to explain.View attachment 22873
First you have to find the length of the blue line. you have to use ' cos' to find it, lets call this line AX
so,
AX= 5c0s0.6 = 4.12 cm
now you will have to find the small length PX. to find PX u need to know the length of AQ, the length of AQ is 5cm because 'BQD' is an arc of a circle with center 'A' so it means its 5cm (the length AQ is the radius of the circle with center A)
so since u know AQ = 5cm, to find PX :
PX = 5 - 4.12 = 0.873 cm
but they are asking us for the length of PQ, so the length is 2*PX
===> PQ = 2*0.837
= 1.75 cm
hope u understood :)
Click to expand...
Thank you so much for the clear explanation :)
 
Alice123

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syed1995 said:
The method i use is very simple.

Just remember two things.

Ex = mean * n
E(number) = number * n

where n is the total number of people or frequency.

n = 24
E(x-36)=-60
Ex-E36=-60
Ex=-60+E36
Ex=-60+(24*36)
Ex=804

E(x-36)^2 = 227.76
E(x^2-72x+1296) = 227.26 (We just opened the square via the (a-b)^2 = a^2 -2ab + b^2
Ex^2-72Ex+E1296 = 227.26
Ex^2=227.76+72(Ex) - E1296
Ex^2=227.76+72(804) - 24*1296
Ex^2=27011.76 or 27000 (3sf)
Click to expand...
thanks a lott :)
 
Alice123

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:)
Dug said:
I assume you have used the following method.
3 : 111
4 : 112, 121, 211
5 : 113, 131, 311, 122, 212, 221
6 : 123, 132, 312, 213, 231, 321, 114, 141, 411, 222

You can make it shorter by using permutation.

3 : 3!/3! = 1
4 : 3!/2! = 3
5 : 3!/2! + 3!/2! = 6
6 : 3!/2! + 3!/2! + 3!/2! + 3!/3! = 10

This can be done by intuition alone. I just showed you the working to make you understand. Hope you got it!!
Click to expand...
thanks again
 
syed1995

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In Case = P(C) = 0.7
Not In Case = P(C`) = 0.3
Finds It = P(F)
CF = 0.7*1
C`F = 0.3*0.2

This question is pretty simple .. Just draw a tree diagram to solve it easily.

The Pen was in his case given that he finds it means.

P(In Case Given He Finds It)= (It was in Case and he finds it) over [ (It was in case and he finds it) + (It was not in case but he still finds it) ]
P(in C given F)= (CF)/(C`F+CF)
= 0.7*1/(0.7*1)+(0.3*0.2)
=0.7/0.7+0.06
=0.7/0.76
 
Alice123

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syed1995 said:
In Case = P(C) = 0.7
Not In Case = P(C`) = 0.3
Finds It = P(F)
CF = 0.7*1
C`F = 0.3*0.2

This question is pretty simple .. Just draw a tree diagram to solve it easily.

The Pen was in his case given that he finds it means.

P(In Case Given He Finds It)= (It was in Case and he finds it) over [ (It was in case and he finds it) + (It was not in case but he still finds it) ]
P(in C given F)= (CF)/(C`F+CF)
= 0.7*1/(0.7*1)+(0.3*0.2)
=0.7/0.7+0.06
=0.7/0.76
Click to expand...
thanks!!! dats simple, i wrote dat by mistake.. i'm sorry. i cudnt solve qs 3
 
syed1995

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Alice123 said:
http://papers.xtremepapers.com/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_s11_qp_61.pdf
no 3 thanks in advance
Click to expand...

This question is really simple.

You need to make a probability distribution table ..

−2, −1, 0, 1, 2, 3, 4, 5

Probability for 0 = 1/10

Probability for any other number = (9/10) / 7 = 9/70

Part 1 is just simple .. add the probabilities of -2,-1,0 and 1.. which is 3*9/70 + 1/10 .. which equals 17/35

Variance = E(X^2)-(EX)^2

Multiply the probability by X and X^2 and add them all to get both the above values.

EX comes as 54/35 and E(X^2) comes as 54/7

Variance = 54/7 - (54/35)^2 = 5.334 Ans

And the last part .. well just see the table and do calculations.. And you will also notice the answer is same as first part.. first part included -2,-1,0,1 .. while this part has -1,0,1,2 .. so a = 1
 
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