Quiz 1

##########
Question 1

x: 1,2,3
px: .2,.6,.2

> x = c(1,2,3)
> px= c(.2,.6,.2)


#####
q1: 

What is P(X > 1) ?

##

.8

> sum(px[x>1])
[1] 0.8

#####
q2:
What is E(X) ?

##
> sum(x*px)
[1] 2


##### 
q3:

What is the standard deviation of X?

> sum((x-2)^2 * px)
[1] 0.4
> sqrt(.4)
[1] 0.6324555


##########
Question 2

Suppose X and Y have the joint distribution give by the following table:

           X
     0          1
  0  .05       .40
Y
  1  .45       .10

So, for example, P(X=0,Y=1) = .45.

##### 
q4: What is P(Y=1) ?

##
.45 + .1 = .55

#####
q5: 

What is P(Y=1 | X=1) ?

##

> .1/(.1+.4)
[1] 0.2

#####
q6: 
true or false:
Y and X are independent.

## 
false

#####
q7: 
true or false:
Y and X are both Bernoulli random variable

##
true

#####
q8: 
true or false:
Y and X are identically distributed 

##
false