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October 19th, 2015, 05:40 AM   #1
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Continuous random variable

Hello everbody i was wondering if anyone could help me out today. My question is



The continous random variable X represents the height in centimetres of a Year 12 male student. A teacher estimates that X possesses the density function

f(x) = (348x-x^2-29700)/18432 for 150 =< x =<198
0 elsewhere

(a) By collecting suitable sufficient data, evaluate the accuracy of this teachers estimated model (empirical test).

(b) Using this data to construct an accurate model of the probability density function possessed by X.



Now this is my train of thoughts so far. What i have done is verified that this is a probability density function. This is true because this definite integral = 0. I also found the expected value of X which was (174) and also the variance of X which was (115.19992)

What's confusing me is that how do i use say some data that i will collect soon to evaluate the model. How do you evaluate a model like this? Also, How do you also go about constructing a probability density function.

Lets just use some radom heights just for the sake of me understanding. Take:

166.1 cm
173.5 cm
188.3 cm
180.4 cm
159.0 cm
163.2 cm
184.8 cm
188.8 cm

can anyone help me use these random data to help me out here?
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October 19th, 2015, 02:39 PM   #2
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Compute the mean and variance of the data and compare with the theory. Also plot the data in histogram form and compare with the theoretic curve.
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