fall08-quiz2 - PROBABILITY AND DECISION MAKING 45-730 REAL...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
PROBABILITY AND DECISION MAKING 45-730 REAL QUIZ 2 (OFFLINE) Problem 1 ( Expectation ) . Consider the following random variables: The random variable X takes the values { 0 , 1 , 2 } with equal probabilities. The random variable Y takes the value 9 with probability 1 3 and 12 with probability 2 3 . The random variable Z takes the values { 2 , 4 , 6 , 8 } with equal probabilities. (1.1) What is the expected value of X ? (1.2) What is the expected value of Y ? (1.3) What is the expected value of Z ? (1.4) What is the expected value of the random variable W = 2 X - Y + 4 Z ? Problem 2 ( Variance ) . Consider the following four random variables. A: Binomial random variable with parameters p = 1 2 ,n = 4. B: Poisson random variable with mean = 1. C: Discrete random variable which taking one of the values 0 , 1 , 2 , 3 , 4 with equal probabilities. D: Discrete random variable which takes value 0 with probability 1 2 and value 4 with probability 1 2 . (2.1) What is the variance of A ? (2.2) What is the variance of B ? (2.3) What is the variance of C ? (2.4) What is the variance of D ? Problem 3 ( ) . A vending machine sells snacks at $0 . 90 each. Let X be the random variable representing the number of snacks sold per day. It is known that
Background image of page 1

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

View Full DocumentRight Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 2

fall08-quiz2 - PROBABILITY AND DECISION MAKING 45-730 REAL...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online