Thread: find cumulative distribution function

plz solve this problem in detail
Consider a random variable X that takes values +1 and -1 with probability 0.5 each. The values of cumulative distribution function F(X) at x=-1 and +1 are....?

(A) 0 and 0.5 (B) 0 and 1 (C) 0.5 and 1 (D) 0.25 and 0.75

Hey balajikcp8.

Hint: The CDF is denoted by P(X <= x) (What can you say about P(X <= -1) and P(X <= +1))?

P(X <= +1)=1. but P(X <= -1)...?

Hint: Including the value -1 (as opposed to not) includes the probability of that observation.

sorry i can't understand. if possible pls explain

Basically P(X <= -1) is the probability that X takes on a value of -1 or anything below -1.

We know that P(X = -1) = 0.5 and P(X <= -1) = P(X < -1) + P(X = -1).

Now P(X = -1) = 0.5 but P(X < -1) = 0 which means P(X <= -1) = 0 + 0.5 = 0.5

Thanks a lot