Random Variables (2 Viewers)

[gamja]

Answers recorded in pencil - I'm not really sure how to integrate in order to find the probabilities for both.
Could someone please shoot some hints my way on how to solve these two questions?

Thanks in advance!

 

[cossine]

View attachment 38587

Answers recorded in pencil - I'm not really sure how to integrate in order to find the probabilities for both.
Could someone please shoot some hints my way on how to solve these two questions?

Thanks in advance!

So was there some mistake with the question it seems you have replace f with F? If this is the case answer should be trivial.

Anyhow do you understand the meaning of the piecewise function notation.

 

[hellopenguin666]

May I know where the question is from?

 

[gamja]

May I know where the question is from?

sorry for the lateness - I don't know where it is from - it was part of a trial paper collection

 

[chilli 412]

View attachment 38587

Answers recorded in pencil - I'm not really sure how to integrate in order to find the probabilities for both.
Could someone please shoot some hints my way on how to solve these two questions?

Thanks in advance!

no need to integrate the cumulative distribution function

and f(x) has domain [a,b]
for some P(X < q), you can just evaluate in F(q) to get the answer, no integration required as it has already been done
for P(X > q), note that this is just 1 - P(X < q) = 1 - F(q)
you can apply this to the first question and use baye's theorem (probability of 'a' given 'b') which is on the reference sheet

 

[chilli 412]

I think 2b) and 2c), the rest is doable

With 2b)

To find Pr(X>=2) it'd be the integral from 2 to infinity of 1 - e^-x^2 but the issue is that you can't integrate that...

I guess you could try doing it with integration by parts (but it's not part of math advanced)

-e^(-x^2) cannot be integrated with respect to x using standard techniques of integration, it is known as the gaussian integral