Answer:
the inter-quartile range will increase
Step-by-step explanation:
The initial data-set was;
20,32,32,45,50
Adding a new value 78 will have several effects;
The mean of the new set of values will increase since 78 is mostly likely to be an outlier.
The median of the new data set will increase. The median of the old data set is 32 while that of the new data set will be 38.5
The mode is the most frequent observation. Both the new and the old sets of values will have a mode of 32. The mode will therefore remain the same.
The inter-quartile range just like the range will increase
What do you mean I need to see the prism ??
The number line should go in this order:
1/4,1/2,3/4, and 2/2
1/4=0.25
1/2=0.5
3/4=0.75
2/2=1
Question #10:
To find what fraction of an onion is used per serving, divide the total amount of onion by the total number servings.
1/2 ÷ 6 = 1/12
Therefore, 1/12 of an onion was used per serving.
Question #12:
1/2 of 3/4 means that we multiply 1/2 to 3/4.
3/4 * 1/2 → 3/8
3/4 of 1/2 means we multiply 3/4 to 1/2.
1/2 * 3/4 → 3/8
Therefore, both expressions are similar.
Best of Luck!
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)
