10. I would like to derive the formula for the volume V of a pyramid with a square base. The pyramid will be drawn sideways, with the x-axis viewed as piercing the center, as drawn below: "Height' = b %3D a It will be formed by treating the thick "diagonal" surface line in the picture as the graph of a function f(x) =-(x-b). f(x) = -%(x – 6) a (a) [ Suppose we have an arbitrary partition of [0, b] into N pieces. Let I; be a small in.erval in our partition, with width Ar; as usual. Find a Riemann Sum approximating the pyramid volume. Your answer should be of the form N V (formula involving some or all of a, b, f, cj, A¤;) j=1 where r = c; indicates some point in the interval I;, as usual. HINTS: A thin vertical slice of the pyramid corresponding to I; looks like a thin disk (but not-circle-shaped... what shape?), with the x-aris piercing the center of the disk. The value of the function f should help determine the volume of such a disk.
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
Question in the pictures below
![10. I would like to derive the formula for the volume V of a pyramid with a square base. The
pyramid will be drawn sideways, with the r-axis viewed as piercing the center, as drawn below:
"Height' = b
It will be formed by treating the thick "diagonal" surface line in the picture as the graph of a
function f(x) = -(x-6).
f(x) = -% (w – b)
a
(a) [ Suppose we have an arbitrary partition of (0, 6] into N pieces. Let I; be a small
inverval in our partition, with width Ar, as usual. Find a Riemann Sum approximating
the pyramid volume. Your answer should be of the form
V (formula involving some or all of a, b, f, cj, Ax;)
j=1
where x =
= C; indicates some point in the interval I,, as usual. HINTS: A thin vertical
slice of the pyramid corresponding to I; looks like a thin disk (but not-circle-shaped... what
shape?), with the x-aris piercing the center of the disk. The value of the function f should
help determine the volume of such a disk.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7ec70b84-8e2a-4846-85d9-f50115a864e8%2F2cc49c63-b061-45f9-af5c-75437a704878%2F0x8lzea_processed.jpeg&w=3840&q=75)
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