Distribution is cumulative addition(discrete)/integration(continuous) of probabilities upto the point of interest. Density is the Probability at the instance of the point.. More generically.. Suppose a species of bacteria typically lives 4 to 6 hours. What is the probability that a bacterium lives exactly 5 hours? The answer is 0%. A lot of bacteria live for approximately 5 hours, but there is no chance that any given bacterium dies at exactly 5.0000000000... hours.
Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is 0.02 (i.e., 2%). Next: What is the probability that the bacterium dies between 5 hours and 5.001 hours? The answer is probably around 0.002, since this is 1/10th of the previous interval. The probability that the bacterium dies between 5 hours and 5.0001 hours is probably about 0.0002, and so on.
In these three examples, the ratio (probability of dying during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour−1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour−1. This quantity 2 hour−1 is called the probability density for dying at around 5 hours.
Therefore, in response to the question "What is the probability that the bacterium dies at 5 hours?", a literally correct but unhelpful answer is "0", but a better answer can be written as (2 hour−1) dt. This is the probability that the bacterium dies within a small (infinitesimal) window of time around 5 hours, where dt is the duration of this window.
For example, the probability that it lives longer than 5 hours, but shorter than (5 hours + 1 nanosecond), is (2 hour−1)×(1 nanosecond) ≃ 6×10−13 (using the unit conversion 3.6×1012 nanoseconds = 1 hour).
There is a probability density function f with f(5 hours) = 2 hour−1. The integral of f over any window of time (not only infinitesimal windows but also large windows) is the probability that the bacterium dies in that window.
please provide answers for digital circuits assignment 10 before due date,i will share to my colloge friends and other college friends ,your blogspot will be famous if you submit assignment answers early
Distribution is cumulative addition(discrete)/integration(continuous) of probabilities upto the point of interest.
ReplyDeleteDensity is the Probability at the instance of the point..
More generically..
Suppose a species of bacteria typically lives 4 to 6 hours. What is the probability that a bacterium lives exactly 5 hours? The answer is 0%. A lot of bacteria live for approximately 5 hours, but there is no chance that any given bacterium dies at exactly 5.0000000000... hours.
Instead we might ask: What is the probability that the bacterium dies between 5 hours and 5.01 hours? Let's say the answer is 0.02 (i.e., 2%). Next: What is the probability that the bacterium dies between 5 hours and 5.001 hours? The answer is probably around 0.002, since this is 1/10th of the previous interval. The probability that the bacterium dies between 5 hours and 5.0001 hours is probably about 0.0002, and so on.
In these three examples, the ratio (probability of dying during an interval) / (duration of the interval) is approximately constant, and equal to 2 per hour (or 2 hour−1). For example, there is 0.02 probability of dying in the 0.01-hour interval between 5 and 5.01 hours, and (0.02 probability / 0.01 hours) = 2 hour−1. This quantity 2 hour−1 is called the probability density for dying at around 5 hours.
Therefore, in response to the question "What is the probability that the bacterium dies at 5 hours?", a literally correct but unhelpful answer is "0", but a better answer can be written as (2 hour−1) dt. This is the probability that the bacterium dies within a small (infinitesimal) window of time around 5 hours, where dt is the duration of this window.
For example, the probability that it lives longer than 5 hours, but shorter than (5 hours + 1 nanosecond), is (2 hour−1)×(1 nanosecond) ≃ 6×10−13 (using the unit conversion 3.6×1012 nanoseconds = 1 hour).
There is a probability density function f with f(5 hours) = 2 hour−1. The integral of f over any window of time (not only infinitesimal windows but also large windows) is the probability that the bacterium dies in that window.
post antennas 6 week solutions
ReplyDeleteplz provide the solution of assignment 1 of analog communication course
ReplyDeleteplease post the assignment of block chain and software testing
ReplyDeleteplease provide answers for digital circuits assignment 10 before due date,i will share to my colloge friends and other college friends ,your blogspot will be famous if you submit assignment answers early
ReplyDelete