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thanks a lot

thanks buddy  for solution

here is important material for exam

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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

Please change it don’t copy as it is

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