Series of S2 questions for S2 Exam next week.

Bump.

2) When defining P.D.F or C.D.F, I don't understand how the limits are done on the right-hand side. Sometimes, they are greater than or equal to and sometimes just greater than, can someone help me out with this? I am really confused. (one on the left)

c.d.f is a continuous function so it doesn't matter if it is the sign is greater than or greater than equal to i.e. 0 <= X < 5 is equal to 0 < X <=5

Whereas p.d.f is a discrete function which means that it only takes in integers like 1,2,3,4,etc so in this case 0 <= X < 5 is equal to 0 <= X <= 4

So, when I convert it from one thing to another, how do I do it? Can you give me some examples?

Suppose limits given is -3 < X <= 5 (this range is any number from -3 to 5 BUT EXCLUDING -3)

For c.d.f you substitute upper limit=5 and lower limit = -3
c.d.f is continuous so the sign doesn't matter anyway

but for p.d.f, it is discrete so you have to convert to -2 <= X <= 5 (you have to convert as p.d.f only takes in integers but the range does not include -3 so the next number to be included is -2.
upper limit would be 5 and lower limit is -2.

Now let's take -3 <= X < 5

for c.d.f upper limit would be 5 and lower limit would be -3

but for p.d.f it converts to -3 <= X <= 4 (as the range does not include 5 so last number to be included is 4)
upper limit=4 and lower limit=-3

So p.d.f s always have =< right?

Yepp

Sorry I can't help with other questions....I have forgotten everything

You see 4.a from the picture above,

The f(x) been defined as 2<=x<3, 0 otherwise, why?

tbh I have no idea why it says so in solutions but I have always done it the way I said

I am so confused what to do then, haha.

Have you try all other questions??
If you do other questions correctly this one might be a typo. There are lots of typo with edexcel textbooks.

Yeah, they all have different ways. I just don't know what I should do.

X

Is that the textbook by James Nicholson? If so, could you tell me if it comes with a CD that has worked solutions (like the official Edexcel series)?

can someone help me with S2 June 2003 Q4 bi please?

It says :A six- sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are likely to appear. The die is thrown repeatedly.

Find the probabilty that :

The first 5 will occur on the sixth throw.

Probability it will be 5= 2/7

Is it (5/7)^5*(2/7)=0.053?

can someone help me with S2 June 2003 Q4 bi please?

It says :A six- sided die is biased. When the die is thrown the number 5 is twice as likely to appear as any other number. All the other faces are likely to appear. The die is thrown repeatedly.

Find the probability that :

The first 5 will occur on the sixth throw.
Probability it will be 5= 2/7

Is it (5/7)^5*(2/7)=0.053?