Binomial probability distribution integration limits

[photon342]

Homework Statement

I am trying to find the limits of integration (upper and lower) of a known value of the binomial probability distribution. In other words, I know what the integral (area under the prob. dist.) needs to be (0.84 and 0.16), but how can I code a function (say into MATLAB) that will take as input the value of the probability, and give me the integration limits?

Homework Equations

the binomial probability distribution - which in kind of lengthy to put in here
the integral of the distribution evaluates the probability of getting a certain value.

The Attempt at a Solution

i've plotted the function in matlab, but don't know how to get the integration limits if the area of the curve in about 68%...
I was thinking some sort of loop, but it may be simpler than that.

 

[mighty2000]

Thank you for your question. I understand that you are trying to find the limits of integration for a known value of the binomial probability distribution. This is a common problem in statistics and can be solved using a few different methods.

One approach is to use the inverse cumulative distribution function (CDF) of the binomial distribution. This function takes a probability as input and returns the corresponding value of the random variable. In your case, you know the desired probability (0.84 and 0.16), so you can use the inverse CDF to find the corresponding values of the random variable. These values will be your upper and lower integration limits.

Another approach is to use a numerical integration method, such as the trapezoidal rule or Simpson's rule, to approximate the integral of the binomial distribution. You can loop through different values of the integration limits until you get the desired probability. This may be more time-consuming, but it can be useful if you do not have access to the inverse CDF function.

I hope this helps you in finding the limits of integration for your problem. Please let me know if you have any further questions.