An experiment that satisfies the following four conditions is called a binomial experiment. 1. There are n identical trials. 2. Each trial has two and only two outcomes. These outcomes are usually called a success and a failure. Each trial is called a Bernoulli trial. 3. P(success) = p, P(failure) = q, and p+q-1. The probabilities p and q remain constant for each trial. 4. The trials are independent. For a binomial experiment, the probability of exactly x successes in n trials is given by the binomial formula P(X = x) = {"}p* q** where n = total number of trials p=probability of success q=1-p=probability of failure x = number of successes in n trials n-x= number of failure in n trials Consider the experiment consisting of 50 tosses of a fair coin and let X be the number of heads. Construct a program in R to show that Xis binomial distributed.

An experiment that satisfies the following four conditions is called a binomial experiment. 1. There are n identical trials. 2. Each trial has two and only two outcomes. These outcomes are usually called a success and a failure. Each trial is called a Bernoulli trial. 3. P(success) = p, P(failure) = q, and p+q-1. The probabilities p and q remain constant for each trial. 4. The trials are independent. For a binomial experiment, the probability of exactly x successes in n trials is given by the binomial formula P(X = x) = {"}p* q** where n = total number of trials p=probability of success q=1-p=probability of failure x = number of successes in n trials n-x= number of failure in n trials Consider the experiment consisting of 50 tosses of a fair coin and let X be the number of heads. Construct a program in R to show that Xis binomial distributed.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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An experiment that satisfies the following four conditions is called a
binomial experiment.
1. There are n identical trials.
2. Each trial has two and only two outcomes. These outcomes are
usually called a success and a failure. Each trial is called a
Bernoulli trial.
3. P(success) = p, P(failure) = q, and p+q=1. The probabilities p
and q remain constant for each trial.
4. The trials are independent.
For a binomial experiment, the probability of exactly x successes in n
trials is given by the binomial formula
where
= (*)p²qx
P(X= x) =
n = total number of trials
p=probability of success
q=1-p=probability of failure
x= number of successes in n trials
n- x= number of failure in n trials
Consider the experiment consisting of 50 tosses of a fair coin and let
X be the number of heads. Construct a program in R to show that Xis
binomial distributed.

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