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)


X = 12.25 and I’m typing this to get to 20 characters
Answer:
Solve for r
−
√
11 < r < √
11
Step-by-step explanation:
The volume of cone shaped popcorn cup is 75.36 cubic inches.
According to the given question.
The height of the popcorn cup = 8inches
And the diameter of the cup = 6 inches
⇒ Radius of the popcorn cup = 6/2 = 3 inches
As we know that, the volume of cone is calculated by the formula
volume of cone = (πr^2h)/3
Therefore, the volume of cone shaped popcorn cup
= 3.14((3)^2)(8)/3
= 3.14(3)(8)
= 75.36 cubic inches
Hence, the volume of cone shaped popcorn cup is 75.36 cubic inches.
Find out more information about volume of cone here:
brainly.com/question/23173618
#SPJ4
Answer:
I got 235, which works in perfectly into the problem...
Step-by-step explanation: