Calculating probability using the CDF function of Beta distribution.

hi,

i need help some help please :(

i have a csv file with some election data (attached it in the post)

and this is the question form my homework:

Using the Beta distribution for each state, you can calculate the probability that the Democrats/Republicans will win the upcom ing elections in each state. Calculate it using the CDF function of each Beta distribution. How and why should you use it to get the probability of the election results in each state?

now i did calculate the beta distribution for each state using this code:

a = data.Democrat + 1; % number of people that voted democrat in the poll

b = data.Republican + 1; % number of people that voted Republican in the poll

% calculating beta distribution for each state_ii :

beta_dist = cell(size(data,1),1); proportion_democrate = zeros;

for ii=1:51

beta_dist{ii} = makedist('beta','a',a(ii),'b',b(ii));

proportion_democrate(ii) = mean(beta_dist{ii});

end

but i dont know how to continue :(

thanks in advance

[the cyclist]

Since this is homework, I'll give you a couple hints on the next step. (There are some important simplifications about the U.S. elections here; I don't know what your teacher expects for details.)

One thing is a bit of knowledge that is important, but I will not assume you know, which is that if a candidate wins a majority of the votes in a state, then they win all the electors for that state. So, the first thing you need to estimate (for each state) is the probability of each party getting getting a majority of the votes.

Hint: You can't just use the proportion of Democrats to do that. You need the CDF, as the assignment says.

[ragad]

first of all thank you so much for your responce :)

and yes I understood that part but Im not sure how to use the cdf function I tried reading about it but I still dont get what input should I put in the function or what the putput means?

[ragad]

my idea was to use the proportion of the democrates and compare it to 0.5 each time. and depending on whether i get 1 or 0 I will conclude if which party won in state i. does that make sense?

[the cyclist]

Sorry, I didn't see that you had replied to my comment.

I did get a notification about the answer below, which looks helpful (although perhaps too late to help for your assignment).

Answer 1

[Rohit]

Hi,

I understand that you want to calculate probability of Democrats/Republicans winning the elections using CDF function of each Beta distribution.

The CDF of a probability distribution gives the probability that a random variable takes a value less than or equal to a certain value. In the case of the beta distribution, the CDF gives the probability that the true proportion of Democrats (or Republicans) in a given state is less than or equal to 0.5, based on the poll data. This is directly related to the probability that the Democrats (or Republicans) will win the upcoming elections in that state, since whoever gets more than 50% of the votes is the winner.

The code you have written is correct and you can follow that by using CDF to get probability as shown below:

% calculate beta distribution for each state 

a = data.Democrat + 1; 

b = data.Republican + 1; 

beta_dist = cell(size(data,1),1); 

proportion_democrat = zeros(size(data,1),1); 

for ii=1:size(data,1) 

    beta_dist{ii} = makedist('beta','a',a(ii),'b',b(ii)); 

end 

% calculate probability of Democrats winning each state 

prob_Dem = zeros(size(data,1),1); 

for ii=1:size(data,1) 

    prob_Dem(ii) = 1 - cdf(beta_dist{ii},0.5); 

end 

% calculate probability of Republicans winning each state 

prob_Rep = 1 - prob_Dem; 

You can learn more about CDF from this documentation link: https://in.mathworks.com/help/stats/prob.normaldistribution.cdf.html