{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

07_Discrete Probability Distributions Part 1

Rolling two dice probability mass function 0000 0028

Info icon This preview shows pages 21–28. Sign up to view the full content.

View Full Document Right Arrow Icon
Rolling Two Dice (Probability Mass Function) 0.000 0.028 0.056 0.084 0.112 0.140 0.168 0.196 2 3 4 5 6 7 8 9 10 11 12 Sum of two dices Probability = = ) 7 ( X P = = ) 7 ( ) 7 ( X P F Rolling Two Dice (Cumulative Distribution) 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 2 3 4 5 6 7 8 9 10 11 12 Sum of two dices Probability
Image of page 21

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

View Full Document Right Arrow Icon
22 More on random variables A random variable is not a fixed number, it can take on a range of values Information on how “large” the random variable is and how “spread out” or “risky” it is can be useful to a decision maker
Image of page 22
23 Expected Value of a Random Variable The mean of a probability distribution A probability-weighted average of possible outcomes. E[X]: Expected value of x x: Values of the random variable P(x): Probability of the random variable taking on the value x. ) ( * ] [ x P x X E X = = μ
Image of page 23

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

View Full Document Right Arrow Icon
24 he expected value is not the most likely outcome! Or even necessarily a possible outcome!) Does not always represent where a majority of value lies. Need to account for the spread of possible values. 50% of the time, the ball hooks 50% of the time, the ball slices On average, the ball should be always on green. Caveat of expected value
Image of page 24
25 Variance and standard deviation of a random variable The variance of a random variable X is the weighted sum of its squared deviation from its mean Standard deviation : the square root of the variance E[X]: Expected value of x x: Values of the random variable P(x): Probability of the random variable taking on the value x. ) ( )] ( [ ] ) [( ] [ 2 2 2 x P X E x X E X Var X X - = - = = μ σ ] [ ] [ X Var X Stdev X = = σ
Image of page 25

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

View Full Document Right Arrow Icon
26 An employee for a vending concession at Wells Fargo Center must choose between working the concession stand and receiving $50 or walking around the stands selling hot dogs on a commission basis. Assume that the employee will make either $90, $70, $45 or $15 selling hot dogs with probabilities 0.1, 0.3, 0.4, and 0.2 respectively. Let the random variable X represent the profit made by the employee selling hot dogs. Define the probability mass function (pmf) for X. 90 0.1 Example: Selling hot dogs at Wells Fargo Center 70 0.3 45 0.4 15 0.2 x P(X=x)
Image of page 26
27 1. Find the expected profit, E[X] when selling hot dogs.
Image of page 27

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

View Full Document Right Arrow Icon
Image of page 28
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