Math Statistics Help?
Posted by admin in Casino on 05 11th, 2010 | one response
Problem 3) Gambling makes people hungry for meat. The restaurant upstairs from the casino advertises 1.0 pound slads of prime rib for only $9.99. But the wiehgt of those prime ribs, described by the random variable “P”, follow the probability density function f(p) = p for 1/2 a) Check that f(p) is an honest p.d.f. b) What is the range of P? c) What is the expectation? d) Find the cumulative distribution function? e) Do you think the median of P is greater than the expectation? Why or why not? f) Would you buy the prime rib? Explain your reasoning in ethical and economic terms?
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a. you need to verify this:
∫(.5, 1.5) p dp = 1
this is not difficult anyway
now clearly
0.5 < f(p) ≤ 1.5
to get the expectation you need to solve
∫(.5, 1.5) x^2 dx
the cumulative distribution on the other hand should be:
∫(.5, x) p dp