Test the following function to determine whether it is a probability function. If it is not, then make it into a probability function. (Give your answers correct to one decimal place.)
R(x) = 0.2, for x = 0, 1, 2, 3, 4
(a) List the distribution of probabilities.
R(0) =0
Changed: Your submitted answer was incorrect. Your current answer has not been submitted.
R(1) =.2
Correct: Your answer is correct.
R(2) =.1 .2/R(2) DIVIDED .2 WHICH WAS X AND DIVIDED INTO THE NUMBER PROVIDED.
Incorrect: Your answer is incorrect.
R(3) =.06
Incorrect: Your answer is incorrect.
R(4) =.05
Incorrect: Your answer is incorrect.
(b) Sketch a histogram. (Do this on paper. Your instructor may ask you to turn in this work
To test whether a function is a probability function, we need to ensure that the sum of all the probabilities equals 1.
(a) List the distribution of probabilities:
Given function: R(x) = 0.2 for x = 0, 1, 2, 3, 4
To check if it is a probability function, let's calculate the probabilities for each value of x:
R(0) = 0.2 (given)
R(1) = 0.2 (given)
R(2) = 0.2 (given)
R(3) = 0.2 (given)
R(4) = 0.2 (given)
So, the distribution of probabilities is:
R(0) = 0.2
R(1) = 0.2
R(2) = 0.2
R(3) = 0.2
R(4) = 0.2
Now, let's check if the sum of probabilities equals 1:
0.2 + 0.2 + 0.2 + 0.2 + 0.2 = 1
Since the sum of probabilities equals 1, the given function is already a probability function.
(b) Sketch a histogram:
To sketch a histogram, we need to show the probabilities on the y-axis and the values of x on the x-axis. Since all the probabilities are the same (0.2), the histogram will have equal columns of the same height representing each value of x (0, 1, 2, 3, 4). The height of each column will be 0.2, and there will be five columns in total.
Please sketch this histogram on paper as instructed.