C09 Probability Distribution

C09 Probability Distribution - Crash course on Probability...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Crash course on Probability Distribution A probability distribution function f ( x ) of a discrete random variable X , is a function that describes the relative likelihood for this random variable to take on a given value . Example (rolling two dice). Let X = the sum of two dice. X is a discrete random variable. Distribution table: x 2 3 4 5 6 7 8 9 10 11 12 # { X = x } f ( x ) Distribution graph: f ( x ) = Pr [ X = x ] f ( x ) 0 for all x Pr [ a X b ] = b X x = a f ( x ) X x f ( x ) = 1 1
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
The expected value or mean of X can be calculated by: μ = E [ X ] = X x xf ( x ) Example (rolling two dice). The standard deviation of X can be calculated by: σ = SD [ x ] = X x ( x - μ ) 2 f ( x ) ! 1 2 σ 2 : variance Example (rolling two dice). (Linearity of expectations) E [ X 1 + X 2 ] = E [ X 1 ] + E [ X 2 ] Example (rolling two dice). A probability distribution function f ( x ) of a continuous random variable X , is a func- tion that describes the relative likelihood for this random variable to take on a given value .
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern