Answer:
The expected value of X is
and the variance of X is 
The expected value of Y is
and the variance of Y is 
Step-by-step explanation:
(a) Let X be a discrete random variable with set of possible values D and probability mass function p(x). The expected value, denoted by E(X) or
, is

The probability mass function
of X is given by

Since the bus driver is equally likely to drive any of the 4 buses, the probability mass function
of Y is given by

The expected value of X is
![E(X)=\sum_{x\in [28,32,42,44]} x\cdot p_{X}(x)](https://tex.z-dn.net/?f=E%28X%29%3D%5Csum_%7Bx%5Cin%20%5B28%2C32%2C42%2C44%5D%7D%20x%5Ccdot%20p_%7BX%7D%28x%29)

The expected value of Y is
![E(Y)=\sum_{x\in [28,32,42,44]} x\cdot p_{Y}(x)](https://tex.z-dn.net/?f=E%28Y%29%3D%5Csum_%7Bx%5Cin%20%5B28%2C32%2C42%2C44%5D%7D%20x%5Ccdot%20p_%7BY%7D%28x%29)

(b) Let X have probability mass function p(x) and expected value E(X). Then the variance of X, denoted by V(X), is
![V(X)=\sum_{x\in D} (x-\mu)^2\cdot p(x)=E(X^2)-[E(X)]^2](https://tex.z-dn.net/?f=V%28X%29%3D%5Csum_%7Bx%5Cin%20D%7D%20%28x-%5Cmu%29%5E2%5Ccdot%20p%28x%29%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2)
The variance of X is
![E(X^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{X}(x)](https://tex.z-dn.net/?f=E%28X%5E2%29%3D%5Csum_%7Bx%5Cin%20%5B28%2C32%2C42%2C44%5D%7D%20x%5E2%5Ccdot%20p_%7BX%7D%28x%29)


The variance of Y is
![E(Y^2)=\sum_{x\in [28,32,42,44]} x^2\cdot p_{Y}(x)](https://tex.z-dn.net/?f=E%28Y%5E2%29%3D%5Csum_%7Bx%5Cin%20%5B28%2C32%2C42%2C44%5D%7D%20x%5E2%5Ccdot%20p_%7BY%7D%28x%29)


Answer:

Step-by-step explanation:
In order to write the series using the summation notation, first we need to find the nth term of the sequence formed. The sequence generated by the series is an arithmetic sequence as shown;
4, 8, 12, 16, 20...80
The nth term of an arithmetic sequence is expressed as Tn = a +(n-1)d
a is the first term = 4
d is the common difference = 21-8 = 8-4 = 4
n is the number of terms
On substituting, Tn = 4+(n-1)4
Tn = 4+4n-4
Tn = 4n
The nth term of the series is 4n.
Since the last term is 80, L = 4n
80 = 4n
n = 80/4
n = 20
This shows that the total number of terms in the sequence is 20
According to the series given 4 + 8 + 12 + 16 + 20+ . . . + 80
, we are to take the sum of the first 20terms of the sequence. Using summation notation;
4 + 8 + 12 + 16 + 20+ . . . + 80 = 
Answer:
False
Step-by-step explanation:
Answer:
9/1 x 3/1
Step-by-step explanation:
Answer:
x^2y^2 3y^2
Step-by-step explanation:
its a or the first choice