Random variables are all around us, from the time we require to commute to school, to the percentage of lecture material we remember for the exam, we can describe much of the world around us using probability.
Project Statement: Find a random variable in your day-to-day life, call it X(w), and do the following:
Describe X as either quantitative, qualitative, discrete, continuous, etc.
Give the support of X (i.e. its possible range of values)
Speculate on its distribution. Is it normal, geometric, exponential, etc.
Give specific reasons and justification for this speculation! Sample this random variable at least 5 times.
Use this sample to estimate its parameters. Give the newly parameterized distribution explicitly.
Solution :
Random variable :-
An example of a random variable in our daily life is time expended in study.
Type of random variable :-
Suppose, random variable X denotes time expended (in hours) in study in a day.
Then X is a continuous random variable.
Support of X :-
X can take any value in the range [0, 24].
Type of distribution :-
Random variable X follows normal distribution.
The causes of such conclusion is as follows.
Our random variable is of continuous type as normal
variate.
In normal distribution, probability is symmetric about mean and
gradually decreases from mean. In case of our proposed random
variable, probability is more or less symmetric about its mean and
gradually decreases from mean.
Sample values :-
Based on previous e days, time expended in study are 12.3, 11.5, 12.0, 11.8 and 11.9 hours.
Estimation of parameters :-
Distribution :-
We found sample mean as 11.9 and sample variance as 0.085.
So, our distribution is as follows.
Project :
Random variables are all around us,from the time we require to commute to school,to the percentage of lecturematerial we remember for the exam,we can desccribe much of the world around us using probability.
Project Statement :
Find a random variable in your day-to-day life,call it x(w),and do the following :
Random variables are all around us, from the time we require to commute to school, to...
please help! 1. Let X One-way commute time to school, and Y- The corresponding time back to home. Commute to School Going Back Home 22-Jan 24-Jan 29-Jan 31-Jan 5-Feb 7-Feb 12-Feb 14-Feb 43 48 45 65 39 48 72 69 63 48 54 49 58 63 82 Propose an unbiased point estimator for μ,- respectively, and define your samples clearly. Construct/derive a (1-α ) 100% C.I. for μ r-14, and specifically based on a random sample of size n, a....
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