Question

This is a programming assignment. You can use any programming language you like You have to submit your computer codes along with the homework. 1. We will now have a look at computer simulations of continuous random variables. (a) Let X be a continuous random variable that is uniformly distributed on 0, 1]. I am sure every one of you can determine actual PDF of X. For warmup, we will try to approximate it using numerical data. For this purpose, we can imagine that the rand function in Octave/Matlab/C returns one realization of X As in the previous homework, we call rand n times to get n values, say (1) 0.134, 0.456, 0.1938944, 0.3928, 0.878, etc. Well, unlike the discrete case, you cannot, for example, take 0.134, and try to count the number of its occurrences in the seguence you generated. as 0.134 will likely happen only once in the entire sequence. This agrees with the fact that P(X a) 0 for any a, when X is a continuous random variable. So, how will you approximate the PDF? The idea is to use a variant of the observation in Page 1 of the book, i.e fx (z) (2) r for small o. So, we can pick some small 5, and consider the intervals (3) for some random variable that we know is distributed on 0,1]. According to (2), we have P (X E 0, 6]) (4) POX E 5, 26]) (5) fx (6) fx and so on. Now, in order to calculate fx I need P(x E D0,81). This I can estimate from the sequence of n numbers I generated. Specifically, POXE 10, would approximately be the number of samples that lie in the interval [0, over the total number of samples, n. In this manner, you can approximate all the terms fx fx (S 5) fx (1- Joining the points (7)
Please answer these questions and please show your code this assignment is all correlated so feel free to use whatever program you'd like. Thank you very much.

Answer 1

Objective-C is the primary programming language you use when writing software for OS X and iOS. It’s a superset of the C programming language and provides object-oriented capabilities and a dynamic runtime. Objective-C inherits the syntax, primitive types, and flow control statements of C and adds syntax for defining classes and methods. It also adds language-level support for object graph management and object literals while providing dynamic typing and binding, deferring many responsibilities until runtime.