ch03t.exe - 0.1 Exercises for Chapter 3 1 An unfair die...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: 0.1 Exercises for Chapter 3 1. An unfair die with six sides is rolled. Let X be outcome of the die. The probability mass function is given to be P(X=i)=i/21 , i=1,2,....6. a) Show that this is a legitimate pmf. b) Find and plot the cumulative distribution function. 2. Put a check-mark in the table below indicating whether or not each of p 1 ( x ), p 2 ( x ), p 3 ( x ) is a legitimate probability mass function (pmf) for the random variable X . x 1 2 3 Is legitimate Is not legitimate p 1 ( x ) .2 .3 .4 .2 p 2 ( x ) .3 .3 .5 -.1 p 3 ( x ) .1 .4 .4 .1 b) Calculate E ( X ) and E (1 /X ) using the following pmf: x 1 2 3 4 p ( x ) .4 .3 .1 .2 c) In a win-win game, the player will win a monetary price, but he/she has to decide between a fixed and a random price. In particular the player is offered $1000 E ( X ) or $1000 X , where the random variable X has the distribution given in (b). When the choice is made a value of X is generated and the player receives the chosen price. Which choice would you recommend the player to make? 3. A metal fabricating plant currently has five major pieces under contract each with a deadline for completion. Let X be the number of pieces completed by their deadlines. Suppose that X is a random variable with p.m.f. p ( x ) given by x 1 2 3 4 5 p ( x ) .05 .10 .15 .25 .35 .10 (a) Find and plot the cdf of X . (b) Use the cdf to find the probability that between one and four pieces, inclusive, are completed by deadline. 1 (c) Find the expectation of X . (d) Find the variance of X . 4. Let X denote the daily sales for a computer manufacturing firm. The cumulative distribution function of the random variable X is F ( x ) = x < . 2 ≤ x < 1 . 7 1 ≤ x < 2 . 9 2 ≤ x < 3 1 3 ≤ x (a) Plot the cumulative distribution function. What is the probability of two or more sales in a day? (b) Write down the probability mass function of X ....
View Full Document

This note was uploaded on 01/11/2012 for the course STAT 401 taught by Professor Akritas during the Fall '00 term at Penn State.

Page1 / 6

ch03t.exe - 0.1 Exercises for Chapter 3 1 An unfair die...

This preview shows document pages 1 - 3. Sign up to view the full document.

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