1. ## Integration & C.P.D

Dear Sir,
I want to understand Integration and Continuous probability distribution here is the question i want the solution with step by step method. Please mention every step & calculation that how it comes?
Q#1 A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1_<x<2
0 elsewhere

a. Show that P(0<X<2)=1
b. Find P(X<1.2).

2. Why do you need integration? It's a triangle with Height = 1 and Base = 2. You can set up the integration if you like.

Notice also how it is nice and symmetrical about the line x = 1. This puts 50% of the probability on each side, making Pr(x < 1.2) = ½ + Pr(1 < x < 1.2). For the last piece, you can:

1) Set up the integration of 2-x on [1,1.2]
2) Remember the area of a trapezoid on [1,1.2]
3) Spot the triangle on [1.2,2] and compute its area, making the desired probabiltiy ½ - (Area of Triangle)

want the solution with step by step method. Please mention every step
This kind of thing always makes me nervous. Maybe you are thinking about it, but it feels like you just want to memorize the procedure rather than understand what you are doing. There is no substitute for understanding. Please review what I said above and see that it is encouragement for you to think about the ideas, not just the processes.

3. ## I need help from attached question

Please see attached file and I want to understand every step.
How X3/3 and answer =1/3 comes?
and also suppose that I am Beginner of mathematics.

4. Originally Posted by nisoo-1
Please see attached file and I want to understand every step.
How X3/3 and answer =1/3 comes?
and also suppose that I am Beginner of mathematics.
they used the power rule to find the integral, and then used the fundamental theorem of calculus to evaluate it between the given limits.

By the power rule: $\displaystyle \int x^n ~dx = \frac {x^{n + 1}}{n + 1} + C$

By the first fundamental theorem of calculus: If F(x) is the integral of f(x) on (a,b), then:

$\displaystyle \int_{a}^{b}f(x)~dx = F(b) - F(a)$

so
$\displaystyle \int_{0}^{1} x^2 ~dx = \left. \frac {x^{2 + 1}}{2 + 1} \right|_{0}^{1}$

$\displaystyle = \left. \frac {x^3}{3} \right|_{0}^{1}$

$\displaystyle = \frac {1^3}{3} - \frac {0^3}{3}$

$\displaystyle = \frac {1}{3}$

5. ## How 2 comes

Sir,
Your method is very understandable. But tell me that how 2 and 1^3/3-0^3/3 calculation comes?

6. Originally Posted by nisoo-1
Sir,
Your method is very understandable. But tell me that how 2 and 1^3/3-0^3/3 calculation comes?
i told you. by the fundamental theorem of calculus. when you want to evaluate an integral between two limits, you plug in the upper limit in the integral formula and then subtract the value you get when you plug in the lower limit into the formula

7. Originally Posted by nisoo-1
Sir,
Your method is very understandable. But tell me that how 2 and 1^3/3-0^3/3 calculation comes?
Get a book on elementary calculus and read it or look at the calculus tutorial
here. It is not pratical for us to teach you how to do elementary definite integrals piece meal.

RonL

8. ## Plz solve question #1

Dear Sir,

Q#1 A continuous random variable X has the density function
f(x)=x for 0<x<1
2-x for 1_<x<2
0 elsewhere

a. Show that P(0<X<2)=1
b. Find P(X<1.2).

9. If you don't understand an answer, provide feedback and conversation. Simply posting again is not useful.

You don't seem to be responding. Please show your work. Please provide background. If you have no idea what an integral is, truthfully, you have no business in calculus-based statistics. Go have a very frank chat with your academic advisor. Something here is not as it should be, perhaps not only your obvious lack of prerequisites.