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Statistics and Probability sta (301)
Question 1:
a) Given the function below
Obtain the value of “c”, so that is a density function.
Solution:
…(a)
First we find the value of c
Now, we put the value of c in equation (a)
Now check that f (x) is a density function.
As we know
So
Hence proved.
b) A random variable “X” following binomial distribution has its mean and variance, 18 and 3.52 respectively. Calculate the value of “n” and “p”.
Solution:
As we know
( p+q)=1
So
As given
So
Question 2:
a) During a laboratory experiment the number of radioactive particles passing through a counter in one milli-second is 4.
I. What is the probability that 6 particles enter the counter in a given milli-second?
II. What is the probability that at most two particles enter the counter in a given milli-second?
Solution:
(i)
As we know x=6
So
(ii)
p(At most two particles enter the counter)=
=
=
=
b) If, then calculate the value of. Where Y is defined as
Solution:
Apply expectation both sides
E (Y)=3E(X)+5 …(a)
Put the value of E (X) in equation (a)
E (Y)=3(5)+5
E (Y)=15
Hence Proved
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