Stats

HW 1

B-1

(c) P(1.4<=X<=4.2)

=p(1)+p(2)+p(3)+p(4)= 0.1+0.3+0.3+0.2=0.9 or 90%

(d) P(1.4<X<4.2)

=p(1)+p(2)+p(3)+(4)= 0.1+0.3+0.3+0.2= 0.9 or 90%

(e) E(X)

= (1)(.1)+2(.3)+3(.3)+4(.2)+5(.1)= 2.9

(f) Var(X)

= (1-2.9)2*0.1+(2-2.9)2*0.3+(3-2.9)2*0.3+(4-2.9)2*0.2+(5-2.9)2*0.1

=3.61*0.1+0.81*0.3+.01*0.3+1.21*0.2+4.41*0.1=1.32

(g) std dev of X= √Var(X)=√1.32=1.15

B-2

(a) E(X)= (a+b)/2=(10+20)/2=15

(b) Var(X)=(b-a)2/12= (20-10)2/12=100/12=8.33

(c) P(X<12) = x-a/b-a=12-10/20-10= 2/10= 0.2 or 20%

(d) P(X>12) = x-b/b-a or 1- P(x<12)= 20-12/10= 0.8 or 80%

(e) P(X<8 or X>22) = 0 as the range is outside of the area under the curve from 10 to 20

B-3

(a) P(X>5) = 1-F(5)= 1-[1-e-5/5]= 1-[1-.368]= 1-.632=.368

(b) P(1.4<=X<=4.2)= F(4.2)-F(1.4)= (1-e4.2/5)-(1-e1.4/5) = (1-.432)-(1-.756)=.568-.244=.324

(c) P(1.4<X<4.2) = F(4.2)-F(1.4)= (1-e4.2/5)-(1-e1.4/5) = (1-.432)-(1-.756)=.568-.244=.324

B-4

A B

1 7.3 mean: 6.38 in excel =SUM(B1:B10)/A10

2 6.1 std dev: 1.47 in excel =STDEV(B1:B10)

3 3.8

4 8.4 variance: 1.472=2.16

5 6.9 95% confidence interval:

6 7.1 6.38+-2.26(1.47/√10) =6.38+-1.05

7 5.3 [5.33, 7.43]- somewhere between with 95% confidence

8 8.2

9 4.9

10 5.8