Statistics 1: Post Your Doubts Here

[Amy Bloom]

Hello there!

I created this thread so that anybody here can post his/her doubts and/or questions in Statistics (1). Hope other people out here will help me and you all.

Feel free to post some notes and any other useful links so that we can help as many people as we can.

Thanks!

 

[Amy Bloom]

I have a question here on topic Discrete Random Variables - Mean & variance of binomial distribution

Five dice are tossed 8 times. Find expected number of times that less than 3 sixes occur in the 5 dice. (Answer should be: 625/81)

 

[Zishi]

I have a question here on topic Discrete Random Variables - Mean & variance of binomial distribution

Five dice are tossed 8 times. Find expected number of times that less than 3 sixes occur in the 5 dice. (Answer should be: 625/81)

It's quite easy if you've done some questions on this topic. You've to think of three possibilities and add them all.
1) 2 sixes = 5C2 times (1/6)^2 times (5/6)^3
2) 1 six = 5C1 times (1/6) times (5/6)^4
3) 0 six = 5C0 times (1/6)^0 times (5/6)^5

Adding these possibilities gives a probability of 625/648. But you're tossing them 8 times. So you've to multiply this by 8 to get your expectation. (625/548) times 8 gives 625/81.

 

[Amy Bloom]

It's quite easy if you've done some questions on this topic. You've to think of three possibilities and add them all.
1) 2 sixes = 5C2 times (1/6)^2 times (5/6)^3
2) 1 six = 5C1 times (1/6) times (5/6)^4
3) 0 six = 5C0 times (1/6)^0 times (5/6)^5

Adding these possibilities gives a probability of 625/648. But you're tossing them 8 times. So you've to multiply this by 8 to get your expectation. (625/548) times 8 gives 625/81.

I completely forgot that! *facepalm*
Thanks pal!

 

[Amy Bloom]

Hello. Can somebody help me with this?? Answers are in squared brackets.

Show that the probability that a point, selected at random inside a circle, is closer to the center of the circle than to the circumference is 1/4.
Points are selected at random inside the circle until a point is closer to the center than to the circumference. What is the probability that:
(i) Exactly three points are selected? [9/64]
(ii) No more than three points are selected? [37/64]
(iii) How many points need to be selected so that there is a probability of at least 0.85 that at least one point is closer to the center than to the circumference? [7]

 

[maryamshake94]

hey.
http://www.xtremepapers.com/papers/...S Level/Mathematics (9709)/9709_w11_qp_61.pdf
5th question here. how do you find the standard deviation in (i)?

 

[Zephyro]

hey.
http://www.xtremepapers.com/papers/CIE/Cambridge International A and AS Level/Mathematics (9709)/9709_w11_qp_61.pdf
5th question here. how do you find the standard deviation in (i)?

94% are within the 12g of the mean. Which means 6% are outside it. Mean is 20 so that would mean the values outside the range would be over 32 or below 8. Either way you have to assume that 3% is below 8 and 3% is above 32.

After that :

P ( X < 32 ) = 32-20 / x

Find the Z value of 0.97 and cross multiply to get the value of x ( SD ).

 

[Amy Bloom]

Can somebody reply my question above please?

 

[Zephyro]

Hello. Can somebody help me with this?? Answers are in squared brackets.

Show that the probability that a point, selected at random inside a circle, is closer to the center of the circle than to the circumference is 1/4.
Points are selected at random inside the circle until a point is closer to the center than to the circumference. What is the probability that:
(i) Exactly three points are selected? [9/64]
(ii) No more than three points are selected? [37/64]
(iii) How many points need to be selected so that there is a probability of at least 0.85 that at least one point is closer to the center than to the circumference? [7]

Exactly 3 points = 3/4 * 3/4 * 1/4

No more than three points are selected = P ( 1,2,3 ) = P(1) + P(2) + (3)

= 1/4+ ( 3/4 * 1/4 ) + (3/4 * 3/4 * 1/4 ) = 37/64

OK, took some time but I got the last quest.

Atleast one point is closer means P(1) or more

P(1) or more = 1 - P(o)

1 - P(0) = 0.85

1 - 3/4^n = 0.85

If you simplify it further by taking log on both sides you will get n > 6.59 or so. The question however wants an exact number so the next closest number is 7.

 

[maryamshake94]

94% are within the 12g of the mean. Which means 6% are outside it. Mean is 20 so that would mean the values outside the range would be over 32 or below 8. Either way you have to assume that 3% is below 8 and 3% is above 32.

After that :

P ( X < 32 ) = 32-20 / x

Find the Z value of 0.97 and cross multiply to get the value of x ( SD ).

umm okayy...thanks.
this is really stupid, but instead of doing the last part can't we use the SD formula? we have x and x bar...

 

[Zephyro]

umm okayy...thanks.
this is really stupid, but instead of doing the last part can't we use the SD formula? we have x and x bar...

You wont get the correct answer. And besides the question is giving you a probability for a reason. They wouldn't give it to you if they didnt think it was needed.

 

[Amy Bloom]

Exactly 3 points = 3/4 * 3/4 * 1/4

No more than three points are selected = P ( 1,2,3 ) = P(1) + P(2) + (3)

= 1/4+ ( 3/4 * 1/4 ) + (3/4 * 3/4 * 1/4 ) = 37/64

OK, took some time but I got the last quest.

Atleast one point is closer means P(1) or more

P(1) or more = 1 - P(o)

1 - P(0) = 0.85

1 - 3/4^n = 0.85

If you simplify it further by taking log on both sides you will get n > 6.59 or so. The question however wants an exact number so the next closest number is 7.

Whoa! I'm impressed . Thank You so much pal. In fact, I didn't understand the question.
Hope you won't mind if i ask you another one : How can you show that the probability that a point, selected at random inside a circle, is closer to the center of the circle than to the circumference is 1/4??
Thanks again.

 

[Zephyro]

Whoa! I'm impressed . Thank You so much pal. In fact, I didn't understand the question.
Hope you won't mind if i ask you another one : How can you show that the probability that a point, selected at random inside a circle, is closer to the center of the circle than to the circumference is 1/4??
Thanks again.

Not sure about that. Would help if you can link me to the past paper to see the exact question.

 

[maryamshake94]

You wont get the correct answer. And besides the question is giving you a probability for a reason. They wouldn't give it to you if they didnt think it was needed.

okayy...
thanks.

 

[Amy Bloom]

Not sure about that. Would help if you can link me to the past paper to see the exact question.

sorry i can't. i got it as a test at school. thank you so much.

 

[Zishi]

sorry i can't. i got it as a test at school. thank you so much.

This about a 'equidistant' circle(which is inside a circle). The distances from midpoint to this circle, and circumference of bigger circle to this one is half the radius of the bigger circle. Using the two "divided" areas, you should be able to get the probability now.

 

[Amy Bloom]

This about a 'equidistant' circle(which is inside a circle). The distances from midpoint to this circle, and circumference of bigger circle to this one is half the radius of the bigger circle. Using the two "divided" areas, you should be able to get the probability now.

huh.... what? sorry if i'm annoying you guys.

 

[Zishi]

Do you understand now what I was trying to say?

 

[Amy Bloom]

Oh! R u saying that there is one small circle in a bigger circle but having the same center?

 

[Amy Bloom]

Do you understand now what I was trying to say?

In fact, i got it b4 u posted the drawing. Thanks for taking the pain.
But then, how do you get the probability?