Question

Find the sample mean, sample median, sample standard deviation, and sample variance of Tthese numbers. 2. A discrete RV has a pdf of the form: P(x) C2, 0,1,2,3. a) What is C? b) What is P(X> 2)? b) What is P(X 2 2)?

Answer 1

12:

(a)

For a valid pdf following must be true:

$\sum_{x=0}^{3}p(x)=1$ ............(1)

Now

$\sum_{x=0}^{3}p(x)=C\cdot (0)^{2}+C\cdot (1)^{2}+C\cdot (2)^{2}+C\cdot (3)^{2}=14C$ ..........(2)

Equating equation (1) and (2) gives

$14C=1$

$C=\frac{1}{14}$

(b)

$P(X> 2)=1-P(X\leq 2)=1-\left [P(X=0)+P(X=1)+P(X=2) \right ]=1-\left [\frac{1}{14}\cdot 0^{2}+\frac{1}{14}\cdot 1^{2}+\frac{1}{14}\cdot 2^{2} \right ]=\frac{9}{14}$

(c)

$P(X\geq 2)=1-P(X< 2)=1-\left [P(X=0)+P(X=1) \right ]=1-\left [\frac{1}{14}\cdot 0^{2}+\frac{1}{14}\cdot 1^{2} \right ]=\frac{13}{14}$