Statistical Analysis Questions Help (1 Viewer)

[csi]

Hi guys,

I need a hand on these questions

1. If the p.d.f. of X is given by f(x) = (1-p)^(x-1)p, 0<p<1, xeJ^+, determine the cumulative distribution function of X.
ANSWER: F(x)=1-(1-p)^x

2. If X1 is a random variable, simplify Var(-X1)
ANSWER: Var(X1)

3. If X1 is a ransomed variable, simplify Var(X1+X1)
ANSWER: 4Var(X1)

Thanks!

 

[Trebla]

Hi guys,

I need a hand on these questions

1. If the p.d.f. of X is given by f(x) = (1-p)^(x-1)p, 0<p<1, xeJ^+, determine the cumulative distribution function of X.
ANSWER: F(x)=1-(1-p)^x

2. If X1 is a random variable, simplify Var(-X1)
ANSWER: Var(X1)

3. If X1 is a ransomed variable, simplify Var(X1+X1)
ANSWER: 4Var(X1)

Thanks!

For the first part, is X meant to be a discrete random variable? If so, the notion of a pdf does not exist. It is actually the pmf (probability mass function).

If so, then we have


The cumulative distribution function is given by



This is the sum of a geometric series which you can then evaluate.

For the second and third part, use the fact that


Substitute X = -X₁ and notice it gives the same variance. Similarly, substitute X = 2X₁ and notice that a factor of 4 comes out.

 

[csi]

For the first part, is X meant to be a discrete random variable? If so, the notion of a pdf does not exist. It is actually the pmf (probability mass function).

If so, then we have


The cumulative distribution function is given by



This is the sum of a geometric series which you can then evaluate.

For the second and third part, use the fact that


Substitute X = -X₁ and notice it gives the same variance. Similarly, substitute X = 2X₁ and notice that a factor of 4 comes out.

Thank you