Math3-http://postimg.org/image/olcodmsyd/?

1
a)
P(1)+P(2)+P(3)+P(4)+P(5)=1
0.1+0.35+0.2+0.15+P(5)=1
P(5)=0.2

b)
P(X>1)
=1-P(1)
=1-0.1
=0.9

(c)
E(X)
=1*0.1+2*0.35+3*0.2+4*0.15+5*0.2
=3.0
E(X^2)
=(1^2)*0.1+(2^2)*0.35+(3^2)*0.2+(4^2)*0.15+(5^2)*0.2
=10.7
Var(X)
=E(X^2)-[E(X)]^2
=10.7-3^2
=1.7

2
E(X)=1*0.1+2*0.4+3*0.2+4*0.3
E(X)=2.7

a)
E(X+3)
=E(X)+3
=2.7+3
=5.7

b)
E(2X-5)
=2E(X)-5
=2(2.7)-5
=0.4

3
E(J or Q)+E(K or A)=E(other cads)
20(8/52)+40(8/52)=n(1-2*8/52)
n=13.3