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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
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a random variable X that takes values +1 and −1 with pr...
The cumulative distribution function
 
F(x) = P(Xx)
F(-1) = P(X-1) = X=-1) =0.5
F(+1)= P(X+1) = P(X=-1)+P(X=-1) = 0.5 + 0.5 =1
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Most Upvoted Answer
Consider a random variable X that takes values +1 and −1 with pr...
Explanation:

Probability Distribution:
- The random variable X takes values +1 and -1 with equal probabilities of 0.5 each.

Cumulative Distribution Function (CDF):
- The cumulative distribution function F(x) gives the probability that the random variable X is less than or equal to a certain value x.
- For X = -1, the CDF F(-1) is the probability that X is less than or equal to -1. Since X can only take values of +1 and -1, the probability that X is less than or equal to -1 is 0.
- For X = +1, the CDF F(1) is the probability that X is less than or equal to +1. Since X can take the value +1 with a probability of 0.5, the CDF F(1) is 0.5.

Conclusion:
- Therefore, the values of the cumulative distribution function F(x) at x = -1 and +1 are 0 and 0.5 respectively. This implies that the correct answer is option C: 0.5 and 1.
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Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values ofthe cumulative distribution function F(x) at x = −1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer?
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Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values ofthe cumulative distribution function F(x) at x = −1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values ofthe cumulative distribution function F(x) at x = −1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Consider a random variable X that takes values +1 and −1 with probability 0.5 each. The values ofthe cumulative distribution function F(x) at x = −1 and +1 area)0 and 0.5b)0 and 1c)0.5 and 1d)0.25 and 0.75Correct answer is option 'C'. Can you explain this answer?.
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