Question

4. Consider a continuous random variable X which has pdf fX(x) = 1/7, 0 < x < 7.

(a) Find the values of µ and σ^ 2 . (You may recognize the model above, and if you do, it is OK to simply write down the answers if you know them.)

(b) A random sample of size n = 28 is taken from the above distribution. Find, approximately, IP(3.3 ≤ X ≤ 3.51). Hint: use the CLT.

Answer 1

Solution

Here X follows uniform distribution with a=0 , b= 7

So it is given by

f(x) = 1/(b-a) ; a<X<b

that is

fX(x) = 1/7, 0 < x < 7

(a) Find the values of µ and σ^ 2

µ = (a+b) / 2

µ = (0+7)/2

µ = 3.5

σ^ 2 = (b-a)2 / 12

σ^ 2 = (7-0)2 / 12

σ^ 2 =4.0833

(b) A random sample of size n = 28 is taken from the above distribution. Find, approximately, IP(3.3 ≤ X ≤ 3.51)