7,095 : 62 = Help me I need it
2 answers:
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Answer:
a)
b)
c)
Step-by-step explanation:
If we work with the limits defined from 5 to 10 then part b and c from this question not makes sense. If we work with the limits 1 and 6 all the parts for the question makes sense because if we work with 5 and 10 the only thing that we can find is the expected value
Assuming the following correct question : "A publication released the results of a study of the evolution of a certain mineral in the Earth's crust. Researchers estimate that the trace amount of this mineral x in reservoirs follows a uniform distribution ranging between 1 and 6 parts per million"
Solution to the problem
Let A the random variable that represent " amount of the mineral x ". And we know that the distribution of A is given by:
Part a
For this uniform distribution the expected value is given by where X is the random variable, and a,b represent the limits for the distribution. If we apply this for our case we got:
Part b
For this case we can use the cumulative distribution function for the uniform distribution given by:
And we want this probability:Part c
For this case we want this probability:
Answer:
I didn't "do the math" yet at all, but draw it out on an X,Y axis... Thinking about it logically... If point A is in the upper right quadrant of the axis, because both X and Y coordinates are positive numbers, so you go right on the horizontal axis and up on the vertical axis... Then the midpoint is in the lower right quadrant of the due to the X coordinate being a positive, thus you go right on the horizontal axis, but the Y coordinate is a negative, so you go down vertically... So point B cannot be above both the midpoint or point A, ruling out (7,7) and (4,5) as both Y coordinates of those answers (7 or 5) are higher than point A's Y coordinate of 2... B would have to be below point A because the midpoint is below point A with a Y coordinate of -3... So this leaves either option (5,-0.5) or option (4,-8)... However.... While (5,-0.5) has a lower Y coordinate than point A with -0.5, its Y coordinate is above the Y coordinate of the midpoint as well, since -0.5 is above -3... So this doesn't jive as point B cannot be between point A and the midpoint to point B... This logically leaves (4,-8) left to be the answer... And if you drew on an X,Y axis the coordinates (6,2) as well as (5,-3) and (4,-8), then connect the dots, you'd find (5,-3) sits about half ways between (6,2) and (4,-8)...
So (4,-8) is probably the answer...
The best way to come to this conclusion mathematically is finding the slope (rise over run) of point A and the midpoint between point A and point B, then continuing the slope down, etc... But this particular question with the multiple choice answers ruled all but 1 answer out...
To find the slope you take rise over run, which is the Y of the 2nd coordinate minus the Y of the 1st coordinate, divided by (or over) the X of the 2nd coordinate minus the X of the 1st coordinate....
IE: ( Y2 - Y1 ) / ( X2 - X1 ) = Rise / Run
So.... The 2nd coordinate's Y value is -3, and the 1st coordinate's Y value is 2... Subtract 2 from -3, and you get -5...
Then the 2nd coordinate's X value is 5, and the first coordinate's X value is 6... Subtract 6 from 5, and you get -1...
Divide -5 over -1, which equals the same as 5 over 1... The rise is 5, the run is 1, the slope is 5 steps vertically for every 1 step horizontally...
Or visually... ( -3 - 2 ) / ( 5 - 6 ) which is -5 / -1... Since both sides are negative, that's the same as 5 / 1... which is 5 vertical steps (rise) for every 1 horizontal step (run), or a slope of 5...
So add the slope rise of 5 to the Y coordinate of the midpoint, -3, and you get 2, which is the Y coordinate of point A... And add slope run of 1 to the midpoint X coordinate, 5, and you get 6, the X coordinate of point A... Now subtract the slope rise of 5 from the midpoint, -3, and you get -8... So that tells you that point B has to have a Y coordinate of -8.... And now subtract the slope run of 1 from the midpoint X coordinate, 5, and you get 4... The X coordinate of point B... Giving you a point B coordinate of (4,-8)...
