Show your work please The probability density function pdf

Show your work please !

The probability density function (pdf) of a discrete random variable x is (1) f(x) = (4 - x)/10, x = 0,1,2,3 Calculate mu, sigma, and sigma2. Find P(x = 2), P(x 2), and P(x 2). Justify whether or not the distribution below is a theoretical probability distribution. (1)

Solution

3) a)

E(x)=sum(x*f(x))=1

var=E(X^2)-(E(X))^2

E(X^2)=sum(X^2*f(x))

E(X^2)=2

var=2-1=1

sd=sqrt(var)=1

b) form the table P(X=2)=0.2

P(X<=2)=P(x=0)+P(X=1)+P(X=2)=0.4+0.3+0.2=0.9

P(X>=2)=P(X=2)+P(X=3)=0.2+0.1=0.3

4)

if sum(p(X))=1, then it is a frequency distirbution.

Since the total is 1, it is a frequency distirbution.

x	f(x)	x*f(x)
0	0.4	0
1	0.3	0.3
2	0.2	0.4
3	0.1	0.3