Logout Open In App
Open In App
Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

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 ≺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 ≺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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

Suppose that a random variableXhas a discrete distribution

with the following p.f.:

\(f\left( x \right) = \left\{ \begin{array}{l}cx\;\;for\;x = 1,...,5,\\0\;\;\;\;otherwise\end{array} \right.\)

Determine the value of the constantc.

Show that there does not exist any numbercsuch that the following function would be a p.f.:

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

Question:Suppose that two persons make an appointment to meet between 5 p.m. and 6 p.m. at a certain location, and they agree that neither person will wait more than 10 minutes for the other person. If they arrive independently at random times between 5 p.m. and 6 p.m. what is the probability that they willmeet?

Suppose that \({{\bf{X}}_{\bf{1}}}\;{\bf{and}}\;{{\bf{X}}_{\bf{2}}}\) are i.i.d. random variables andthat each of them has a uniform distribution on theinterval [0, 1]. Find the p.d.f. of\({\bf{Y = }}{{\bf{X}}_{\bf{1}}}{\bf{ + }}{{\bf{X}}_{\bf{2}}}\).

In a large collection of coins, the probability X that a head will be obtained when a coin is tossed varies from one coin to another, and the distribution of X in the collection is specified by the following p.d.f.:

\({{\bf{f}}_{\bf{1}}}\left( {\bf{x}} \right){\bf{ = }}\left\{ {\begin{align}{}{{\bf{6x}}\left( {{\bf{1 - x}}} \right)}&{{\bf{for}}\,{\bf{0 < x < 1}}}\\{\bf{0}}&{{\bf{otherwise}}}\end{align}} \right.\)

Suppose that a coin is selected at random from the collection and tossed once, and that a head is obtained. Determine the conditional p.d.f. of X for this coin.
See all solutions

Recommended explanations on Math Textbooks

Calculus

Read Explanation

Mechanics Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Applied Mathematics

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.

Sign-up for free