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 12.5k views answer comment Share Follow See all 6 Comments See all 6 6 Comments reply deone commented Dec 4, 2020 reply Follow Share this might be helpful to understand the Cumulative distribution function. https://en.wikipedia.org/wiki/Cumulative_distribution_function 0 votes 0 votes Nirmal Gaur commented Feb 5, 2021 reply Follow Share https://www.probabilitycourse.com/chapter3/3_2_1_cdf.php 0 votes 0 votes Arthu commented Jul 12, 2021 reply Follow Share and watch the other 2 videos in the series as well 3 votes 3 votes 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 53 votes 53 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 Show 16 previous comments 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.