Answer to Question #181037 in Statistics and Probability for phemelo mongae

Question

A psychologist who is conducting learning experiments with rats has prepared a simple web with just two narrow paths through it. When the rat is introduced into the web, it must go down one of the paths. One leads to food, the other does not. Each rat is introduced to the same web three times, and an outcome on each trial is noted. (i) Give a suitable sample space for this experiment. (ii) Let the random variable X be the number of times the rat succeeds in reaching the food. Give the distribution table for the realizations of X. and (iii) Find the Cumulative distribution function (cdf) for X. (iv) Graph the The pdf and cdf for random variable x, the number of times the rat succeeds in reaching the food 

Answer 1

Let the paths are 1 and 2

And F denote Food and O denote others.

(i) Sample space={1F,1O,2F,2O,3F,3O}

(ii) The distribution for X is given by-

(iii) Cummulative distribution function $(CDF)= \int_{0}^4f(x)dx$

where $f(x)$ = Probability Density function

(iv)