Estimators for Functions of the Probability of Success in a Sequence of Bernoulli Trials

1975 ◽  
Vol 4 (10) ◽  
pp. 941-953
Author(s):  
Donald Bamber
Author(s):  
J. E. A. Dunnage

1. Introduction. Bernoulli trials. Consider a sequence of Bernoulli trials. Let p, assumed to satisfy 0<p < 1, be the probability of success at any given trial and let q = 1–p. If Nn is the number of successes in the first n trials, it is well known that Nn/n→p almost surely as n→∞ so that for every ∈> 0,as n→∞, and it is clearly of great interest to know quantitatively how this probability depends upon n and ∈.


2008 ◽  
Vol 45 (3) ◽  
pp. 901-906 ◽  
Author(s):  
Lars Holst

In a sequence of independent Bernoulli trials the probability of success in the kth trial is pk = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.


2008 ◽  
Vol 45 (03) ◽  
pp. 901-906 ◽  
Author(s):  
Lars Holst

In a sequence of independent Bernoulli trials the probability of success in the kth trial is p k = a / (a + b + k − 1). An explicit formula for the binomial moments of the number of two consecutive successes in the first n trials is obtained and some consequences of it are derived.


2017 ◽  
Vol 33 (5) ◽  
pp. 318-327
Author(s):  
Philipp Alexander Freund ◽  
Vanessa Katharina Jaensch ◽  
Franzis Preckel

Abstract. The current study investigates the behavior of task-specific, current achievement motivation (CAM: interest in the task, probability of success, perceived challenge, and fear of failure) across a variety of reasoning tasks featuring verbal, numerical, and figural content. CAM is conceptualized as a state-like variable, and in order to assess the relative stability of the four CAM variables across different tasks, latent state trait analyses are conducted. The major findings indicate that the degree of challenge a test taker experiences and the fear of failing a given task appear to be relatively stable regardless of the specific task utilized, whereas interest and probability of success are more directly influenced by task-specific characteristics and demands. Furthermore, task performance is related to task-specific interest and probability of success. We discuss the implications and benefits of these results with regard to the use of cognitive ability tests in general. Importantly, taking motivational differences between test takers into account appears to offer valuable information which helps to explain differences in task performance.


Sign in / Sign up

Export Citation Format

Share Document