Question

5 numbers chosen randomly without replacement. (#'s range 1-39). "B" represents number of even numbers, this random variable has this probability:

x	0	1	2	3	4	5
p(B=x)	0.02693	0.15989	.33858	.31977	.13464	.02020

number of odd #s chosen would then be 5-x, if x is even #s chosen. "C" represents difference b/w # of even and # of odd chosen, --> C= 2B-5

a. show how variance of B is = 1.1177

b. what is SD of "B"?

c. what is mean of "C" = ?

d. what is variance of "C" = ?

Answer 1

Please don't hesitate to give a "thumbs up" for the answer in case the answer has helped you

a.

I have calculated the Var(x) as E(x^2) - E(x)^2

E(x) is calculated as x weighted by p(B=x)

Also, E(x^2) is x^2 weighted by P(B=x)

X	p(B=x)	E(x)	x^2	E(x^2)	Var(x)
0	0.02693	2.43592	0	7.05138	1.117674
1	0.15989		1
2	0.33858		4
3	0.31977		9
4	0.13464		16
5	0.0202		25

Var(x) = 1.117674 or 1.1177 ( as seen in last column)

b.

SD is nothing but the square root of variance

= sqrt(1.117674)

= 1.0572

c. C = 2B-5

Mean(C)

= Mean(2B-5)

= 2*Mean(B) - Mean(5)

= 2*E(x) - 5

= 2*2.43592 - 5

= -0.12816

d. Var(2B-5)

= Var(2B) + Var(5)

= 4*Var(B) + 0

= 4*1.117674

= 4.4707