You are Here: Home >< Maths

# valid cumulative distribution functions Watch

1. (Refer to image) I don't understand how to get part a of this question

I realize to be a valid CDF, it must satisfy: F(a)=0 and F(b)=1 and I evaluated the functions in (a) at the endpoints of its domain and ended up with a pair of simultaneous equations : a(b-1)^2 = 1 and a(b+1)^2 = 0

to which I got this result when I expanded and solved simultaneously:
2ab^2 + 2a -1=0. Not sure how to solve that for a and b though?

If we solve a(b+1)^2 = 0 we get b=-1 (which is right), which when substituted into the 1st equation a(b-1)^2 = 1 gives the correct value (according to the answer) for a= 0.25.

But wouldn't a(b+1)^2 = 0 also imply that a=0?
2. (Original post by zomgleh)
(Refer to image) I don't understand how to get part a of this question

I realize to be a valid CDF, it must satisfy: F(a)=0 and F(b)=1 and I evaluated the functions in (a) at the endpoints of its domain and ended up with a pair of simultaneous equations : a(b-1)^2 = 1 and a(b+1)^2 = 0

to which I got this result when I expanded and solved simultaneously:
2ab^2 + 2a -1=0. Not sure how to solve that for a and b though?

If we solve a(b+1)^2 = 0 we get b=-1 (which is right), which when substituted into the 1st equation a(b-1)^2 = 1 gives the correct value (according to the answer) for a= 0.25.

But wouldn't a(b+1)^2 = 0 also imply that a=0?
No. The answer is in your question.

Indeed, under normal circumstances

but you have a second constraint. Namely

This equation has to be true at the same time.
3. (Original post by Indeterminate)
No. The answer is in your question.

Indeed, under normal circumstances

but you have a second constraint. Namely

This equation has to be true at the same time.
just seen this, thank you!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 10, 2013
Today on TSR

### Anxious about my Oxford offer

What should I do?

### US couple arrested - 13 children chained up

Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• Poll
Useful resources

## Make your revision easier

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams

Can you help? Study help unanswered threads

## Groups associated with this forum:

View associated groups
Discussions on TSR

• Latest
• ## See more of what you like on The Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

• The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE
{"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}