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GATE CSE 2012 | Question: 21

20,693 views
61 61 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

  1. $0$ and $0.5$
  2. $0$ and $1$
  3. $0.5$ and $1$
  4. $0.25$ and $0.75$

6 Answers

Best answer
74 74 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: $C$
• edited by
21 21 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

4 4 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

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