Student ID: CIIT/SP15-RPM-065/CVCStudent Name: Muhammad Tariq
WaseemMGT601 Statistical InferenceAssignment No. 1Question No. 1:An
integer is chosen at random from the first 200 positive integers.
What is the probability that the integer chosen is divisible by 6
or by 8?Solution:
The sample space for the given experiment is
Therefore, number of sample points in are,
Let
And
Therefore,
and number of sample points in are,
And
and number of sample points in are,
Now checking whether events and are mutually exclusive,
and number of sample points in are,
Since events and are not mutually exclusive, as , hence, formula
to calculate the probability that the integer chosen is divisible
by 6 or by 8 is as under:
Where,
Now,
Thus the probability of the integer chosen at random from the
first 200 positive integers is 0.25 that it is divisible by 6 or by
8.Question No. 2:If X is a Poisson distribution random variable
with parameters =2, find the probabilities for x= 0,1,2,3 or
more?Solution:
Given parameter represents mean which is
Since the mean of a Poisson random variable represents parameter
, therefore,
The formula for Poisson distribution is,
Therefore desired probabilities for are as under:
