/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q1E Suppose that a random variable X... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 3: Q1E (page 116)

Suppose that a random variable X has the Bernoulli distribution with the parameter p = 0.7. (See Definition 3.1.5.) Sketch the c. d. f. of X.

Short Answer

Expert verified

P(X 鈮�1) = 0.3

Step by step solution

01

Given the information

A random variable X has the Bernoulli distribution with parameter p=0.7

02

Statement and find the c. d. f of X

A random variable Z that takes only two values, 0 and 1, with P(Z=1) = p, has the Bernoulli distribution with parameter p. Z is sometimes referred to as a Bernoulli randomized variable with value p.

The formula for c. d. f. of X

03

Calculations

Then we have given that it has a Bernoulli distribution with parameter p=0.7 means P(X=1) = 0.7, the equation that says

P(X 鈮�1) = 0.3

So, the c. d. f. would be 0 before x=0, then to 0.3, and then at x=1, it would be up to1

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Question:A painting process consists of two stages. In the first stage, the paint is applied, and in the second stage, a protective coat is added. Let X be the time spent on the first stage, and let Y be the time spent on the second stage. The first stage involves an inspection. If the paint fails the inspection, one must wait three minutes and apply the paint again. After a second application, there is no further inspection. The joint pdf.of X and Y is

\(f\left( {x,y} \right) = \left\{ \begin{array}{l}\frac{1}{3}if\,1 < x < 3\,and\,0 < y < 1\\\frac{1}{6}if\,1 < x < 3\,and\,0 < y < 1\,\\0\,\,otherwise.\\\,\end{array} \right.\,\,\)

a. Sketch the region where f (x, y) > 0. Note that it is not exactly a rectangle.

b. Find the marginal p.d.f.鈥檚 of X and Y.

c. Show that X and Y are independent.

Suppose that the p.d.f. of a random variable X is as

follows:\(f\left( x \right) = \left\{ \begin{array}{l}\frac{1}{2}x\,\,\,\,\,\,\,\,for\,0 < x < 2\\0\,\,\,\,\,\,\,\,\,\,\,\,otherwise\end{array} \right.\)

Also, suppose that \(Y = X\left( {2 - X} \right)\) Determine the cdf and the pdf of Y .

Suppose that a random variableXhas the uniform distribution on the interval [鈭�2,8]. Find the p.d.f. ofXand the value of Pr(0<X <7).

Let Xbe a random variable for which the p.d.f. is as in Exercise 5. After the value ofXhas been observed, letYbe the integer closest toX. Find the p.f. of the random variableY.

Question:Suppose that a point (X,Y) is to be chosen from the squareSin thexy-plane containing all points (x,y) such that 0鈮�x鈮�1 and 0鈮�y鈮�1. Suppose that the probability that the chosen point will be the corner(0,0)is 0.1, the probability that it will be the corner(1,0)is 0.2, and the probability that it will be the corner(0,1)is 0.4, and the probability that it will be the corner(1,1)is 0.1. Suppose also that if the chosen point is not one of the four corners of the square, then it will be an interior point of the square and will be chosen according to a constant p.d.f. over the interior of the square. Determine

\(\begin{array}{l}\left( {\bf{a}} \right)\;{\bf{Pr}}\left( {{\bf{X}} \le \frac{{\bf{1}}}{{\bf{4}}}} \right)\;{\bf{and}}\\\left( {\bf{b}} \right)\;{\bf{Pr}}\left( {{\bf{X + Y}} \le {\bf{1}}} \right)\end{array}\)
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Logic and Functions

Read Explanation

Decision Maths

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Pure Maths

Read Explanation

Probability and Statistics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.