41 votes 41 votes Consider a random variable $X$ that takes values $+1$ and $−1$ with probability $0.5$ each. The values of the cumulative distribution function $F(x)$ at $x = −1$ and $+1$ are $0$ and $0.5$ $0$ and $1$ $0.5$ and $1$ $0.25$ and $0.75$ Probability gatecse-2012 probability random-variable easy + – Arjun asked Sep 24, 2014 Arjun 12.6k views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply Show 3 previous comments raja11sep commented Jan 24, 2022 reply Follow Share The Cumulative Distribution Function (CDF), of a real-valued random variable X, evaluated at x, is the probability function that X will take a value less than or equal to x. 1 votes 1 votes raja11sep commented Jan 24, 2022 reply Follow Share cumulative distribution function can be continuous or discrete, Whatever it is the answer will not change here. 0 votes 0 votes JAINchiNMay commented Sep 26, 2022 reply Follow Share @Arthu the videos are very useful 2 votes 2 votes Please log in or register to add a comment.
Best answer 54 votes 54 votes Given $P(-1) = 0.5$ and $P(1) = 0.5$. So, at all other points P must be zero as the sum of all probabilities must be 1. $So, F(-1) = 0.5$ and $F(1) = P(-1) + 0 + 0 + ... + P(1)$ = $0.5 + 0.5 = 1$ Correct Answer: $C$ Arjun answered Sep 25, 2014 • edited Apr 25, 2019 by Naveen Kumar 3 Arjun comment Share Follow See all 19 Comments See all 19 19 Comments reply Priyabrata Mallick 1 commented Jul 18, 2015 reply Follow Share @Arjun Sir as value of the random variables are only +1 and -1, So I thinks we should not consider the other points between -1 and +1. right ? 0 votes 0 votes Arjun commented Jul 19, 2015 reply Follow Share It is not told that random variables take only 2 values. But instead told that probability of 2 values sum to 1. So, probability of other points must be 0. Even if we consider 2 points only, we get the answer. 10 votes 10 votes Aspi R Osa commented Jan 7, 2016 reply Follow Share what is the formula of F(x)? 0 votes 0 votes Arjun commented Jan 7, 2016 reply Follow Share It is the sum of all probability distribution values till the given point $x$. Use integration for continuous probability and summation for discrete. As the probability distribution function changes (like for uniform, poisson etc.) this formula also changes. This question does not require any formula or there is no use even if one had known all such formula. (One reason why I say formula are not important for GATE). 17 votes 17 votes Akriti sood commented Jun 30, 2016 reply Follow Share @arjun sir,can you suggest a good site for knowledge of probability distribution functions and ol 0 votes 0 votes Arjun commented Jun 30, 2016 reply Follow Share All good links I find are updated in respective subject pages in gatecse under weblinks- you can see here: http://gatecse.in/probability/ 1 votes 1 votes vaishali jhalani commented Nov 16, 2016 reply Follow Share @arjun Sir....For F(-1) we have to consider all the points from neg infinity to -1 and same for F(1)? 0 votes 0 votes Arjun commented Nov 16, 2016 reply Follow Share Yes, as per definition. 0 votes 0 votes sushmita commented Jan 26, 2017 reply Follow Share F(1) = P(-1) + 0 + 0 + ... + P(1) = 0.5 + 0.5 = 1 why so?? I am unable to understand. Plz explain :( 1 votes 1 votes Arjun commented Jan 26, 2017 reply Follow Share That is completely theoretical. Intuitively we can say that sum of probabilities across all possible values is always 1. So if probability at two points are 0.5 each, then at all other points it must be 0. Now cumulative probability is nothing but sum of probabilities of all points till the given one. 17 votes 17 votes sushmita commented Jan 28, 2017 reply Follow Share Thanx arjun sir :) 1 votes 1 votes AmitPatil commented Feb 5, 2017 reply Follow Share Is it in GATE 2017 syllabus? 0 votes 0 votes sushmita commented Feb 5, 2017 reply Follow Share Why not? 1 votes 1 votes AmitPatil commented Feb 5, 2017 reply Follow Share In syllabus only 5 distributions are mentioned. Binomial Poissons Uniform Exponential Normal Is cumulative dis. is subcategory of any of these? I never read about cumulative dis. So I am asking you... 0 votes 0 votes sushmita commented Feb 5, 2017 reply Follow Share You are right. Officially it shouldn't be asked but it's just a 5 min thing. But yeah it's not in syllabus. 1 votes 1 votes Arjun commented Feb 5, 2017 reply Follow Share It is in syllabus. The 5 given in syllabus are probability distribution functions and for each of them we have the cumulative distribution function. 16 votes 16 votes Madhab commented Nov 6, 2017 reply Follow Share Sir IN the GATECSE PROBABILITY 2 links that are FORMULA FOR DISTRIBUTIONS AND NOTES FOR DISTRIBUTIONS ARE NOT opening. 0 votes 0 votes Appu B commented Jan 4, 2018 reply Follow Share probability distribution http://web.archive.org/web/20151010091326/http://web.stanford.edu:80/~iwright/PP%20Materials/Lesson%206%20Probability%20Distributions%20Notes.pdf 3 votes 3 votes akankshadewangan24 commented Mar 9, 2018 reply Follow Share Sir I m confused about f(x) at c -1 is .5 why???? @Arjunsir 0 votes 0 votes Please log in or register to add a comment.
12 votes 12 votes Probability x=-1 0.5 x=1 0.5 F(X) is the cumulative distribution function and let P is the probability and given X is random variable so The formula for cumulative distribution function is F(X)=P(X<=x) F(-1)=P(X<=-1) = P(x=-1) =0.5 and F(1)=P(X<=1) =P(x=-1)+P(x=1) =0.5 + 0.5 =1 Anit Pratap answered Aug 7, 2020 Anit Pratap comment Share Follow See all 0 reply Please log in or register to add a comment.
6 votes 6 votes CORRECT ANS – (C) Sayanm_16 answered Apr 22, 2023 Sayanm_16 comment Share Follow See all 0 reply Please log in or register to add a comment.
2 votes 2 votes F(X) is the cumulative distribution function and let P is the probability and given X is random variable so The formula for cumulative distribution function is F(X)=P(X<=x) F(x) = P(X≤x) F(-1) = P(X≤-1) = P(X=-1) = 0.5 F(+1) = P(X≤+1) = P(X=-1) + (P=+1) = 0.5+0.5 = 1 Correct Answer: C akshay_123 answered Sep 4, 2023 akshay_123 comment Share Follow See 1 comment See all 1 1 comment reply akshay_123 commented Sep 4, 2023 reply Follow Share ok 0 votes 0 votes Please log in or register to add a comment.