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probability and statistics for economists

 
 
Reply Sun 7 Dec, 2014 04:39 pm
A psychologist has estimated that either 1,2, or 3 hours of examination is required
to properly assess the case of a new patient. Allow X to be a random variable indicating
the time in hours that it takes with a patient to complete this task. The following
probability function has been proposed.
f (x) = x / 6 for x = 1,2 or 3
a) Is this a discrete or a continuous probability function? Explain.
b) Does this function satisfy the axioms of probability? Explain.
c) Give the cumulative density function.
d) Use the cumulative density function to determine the probability that it takes exactly 2
hours to complete the task.
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raprap
 
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Reply Sat 13 Dec, 2014 05:55 am
@armandok,
A is 1 hour, B is 2 hour, C is 3 hour

With probability function of six permutations of patient ABC, BAC,CAB,CBA, BCA,ACB (this is where it is discreet)

Prob function 1/6,1/3,1/2 (1,2,3) out of any 6 patients

ABC=1*1+2*2+3*3=14
BAC=1*2+2*1+3*3=13
CAB=1*3+2*1+3*2=11
CBA=1*3+2*2+3*1=10
BCA=1*2+2*3+3*1=11
ACB=1*1+2*3+3*2=13

Add em all up=14+13+11+10+11+13=14+2*13+2*11+10=24+26+22=72 hours total for all permutations.

As there are 6 permutations 72/6=12 hours spent on any 6 patients.

and 12/6=2 hr


Rap


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