GATE CSE 2012 | Question: 21

Question

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

• A. $0$ and $0.5$
• B. $0$ and $1$
• C. $0.5$ and $1$
• D. $0.25$ and $0.75$

Comments

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.

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cumulative distribution function can be continuous or discrete, Whatever it is the answer will not change here.

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@Arthu the videos are very useful

Answer 1

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: $C$

Comments

Sir IN the GATECSE PROBABILITY  2 links that are FORMULA FOR DISTRIBUTIONS AND NOTES FOR DISTRIBUTIONS ARE NOT opening.

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probability distribution

http://web.archive.org/web/20151010091326/http://web.stanford.edu:80/~iwright/PP%20Materials/Lesson%206%20Probability%20Distributions%20Notes.pdf

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Sir I m  confused about f(x) at c -1 is .5 why????  @Arjunsir

Answer 2

       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

Answer 3

CORRECT ANS – (C)

Answer 4

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

Comments

ok