Answer:
![V(X) = E(X^2)-[E(X)]^2=349.2-(18.6)^2=3.24](https://tex.z-dn.net/?f=V%28X%29%20%3D%20E%28X%5E2%29-%5BE%28X%29%5D%5E2%3D349.2-%2818.6%29%5E2%3D3.24)
The expected price paid by the next customer to buy a freezer is $466
Step-by-step explanation:
From the information given we know the probability mass function (pmf) of random variable X.
<em>Point a:</em>
- The Expected value or the mean value of X with set of possible values D, denoted by <em>E(X)</em> or <em>μ </em>is
Therefore
- If the random variable X has a set of possible values D and a probability mass function, then the expected value of any function h(X), denoted by <em>E[h(X)]</em> is computed by
![E[h(X)] = $\sum_{D} h(x)\cdot p(x)](https://tex.z-dn.net/?f=E%5Bh%28X%29%5D%20%3D%20%24%5Csum_%7BD%7D%20h%28x%29%5Ccdot%20p%28x%29)
So 
and
![E[h(X)] = $\sum_{D} h(x)\cdot p(x)\\E[X^2]=$\sum_{D}x^2\cdot p(x)\\ E(X^2)=16^2\cdot 0.3+18^2\cdot 0.1+20^2\cdot 0.6\\E(X^2)=349.2](https://tex.z-dn.net/?f=E%5Bh%28X%29%5D%20%3D%20%24%5Csum_%7BD%7D%20h%28x%29%5Ccdot%20p%28x%29%5C%5CE%5BX%5E2%5D%3D%24%5Csum_%7BD%7Dx%5E2%5Ccdot%20p%28x%29%5C%5C%20E%28X%5E2%29%3D16%5E2%5Ccdot%200.3%2B18%5E2%5Ccdot%200.1%2B20%5E2%5Ccdot%200.6%5C%5CE%28X%5E2%29%3D349.2)
- The variance of X, denoted by V(X), is
![V(X) = $\sum_{D}E[(X-\mu)^2]=E(X^2)-[E(X)]^2](https://tex.z-dn.net/?f=V%28X%29%20%3D%20%24%5Csum_%7BD%7DE%5B%28X-%5Cmu%29%5E2%5D%3DE%28X%5E2%29-%5BE%28X%29%5D%5E2)
Therefore
![V(X) = E(X^2)-[E(X)]^2\\V(X)=349.2-(18.6)^2\\V(X)=3.24](https://tex.z-dn.net/?f=V%28X%29%20%3D%20E%28X%5E2%29-%5BE%28X%29%5D%5E2%5C%5CV%28X%29%3D349.2-%2818.6%29%5E2%5C%5CV%28X%29%3D3.24)
<em>Point b:</em>
We know that the price of a freezer having capacity X is 60X − 650, to find the expected price paid by the next customer to buy a freezer you need to:
From the rules of expected value this proposition is true:
We have a = 60, b = -650, and <em>E(X)</em> = 18.6. Therefore
The expected price paid by the next customer is
Answer:
a) 2/42
b)16/42
Step-by-step explanation:
a) 2/7 x 1/6 = 2/42
b) (1,2) (1,3) (2,3)
P(1,2) = 2/7 x 3/6 = 6/42
P(1,3) = 2/7 x 2/6 = 4/42
P(2,3) = 3/7 x 2/6 = 6/42
Add all = 6/42 + 4/42 + 6/42 = 16/42
Answer:7
Step-by-step explanation:
This can be solved by Venn-diagram
Given there are total 5 students who want french and Latin
also 3 among them want Spanish,french & Latin
i.e. only 2 students wants both french and Latin only.
Also Student who want only Latin is 5
Thus Student who wants Latin and Spanish both only is 11-5-3-2=1
Students who want only Spanish is 8 Thus students who wants Spanish and French is 4
Similarly Students who wants Only French is 16-4-3-2=7
Answer:
0.16km
Step-by-step explanation:
Unless I am missing something it is a simple subtraction problem and the time is not needed. It is simply asking how much farther Avery ran than Max, which is 1.61km - 1.45km which is 0.16km
A hummingbird flies at an average speed of 25-30 miles per hour and can do a fast dive at up to 60 miles per hour. A: Yes. A cheetah will run at about 70 miles per hour and a hummingbird flies at about 25-30 miles per hour.
