Electrical Engineering (EE) Exam  >  Electrical Engineering (EE) Questions  >  Consider a random variable x that takes value... Start Learning for Free
Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value 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 1
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a random variable x that takes values +1 and -1 with probabil...
The PDF of the random variable is

The cumulative distribution function F(x) is the probability upto x as given below
View all questions of this test
Most Upvoted Answer
Consider a random variable x that takes values +1 and -1 with probabil...
The cumulative distribution function (CDF) gives the probability that a random variable takes on a value less than or equal to a given value. In this case, the random variable x takes values of 1 and -1 with equal probability of 0.5 each. Let's calculate the CDF for both values.

Calculating CDF for x = -1:
The CDF at x = -1, denoted as F(-1), is the probability that x takes on a value less than or equal to -1. Since x can only take on the values 1 and -1, we need to calculate the probability that x is less than or equal to -1, which is P(x ≤ -1).

Since x can only take on the values 1 and -1 with equal probability, the probability that x is less than or equal to -1 is equal to the probability that x is equal to -1, which is 0.5.

Therefore, F(-1) = P(x ≤ -1) = 0.5.

Calculating CDF for x = 1:
Similarly, the CDF at x = 1, denoted as F(1), is the probability that x takes on a value less than or equal to 1. We need to calculate P(x ≤ 1).

Since x can only take on the values 1 and -1 with equal probability, the probability that x is less than or equal to 1 is equal to the probability that x is equal to 1, which is also 0.5.

Therefore, F(1) = P(x ≤ 1) = 0.5.

Conclusion:
The CDF for x = -1 is 0.5, and the CDF for x = 1 is also 0.5. Therefore, the correct answer is option 'C', which states that the value of the cumulative distribution function F(x) at x = -1 and 1 is 0.5 and 0.5 respectively.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer?
Question Description
Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 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 value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer?.
Solutions for Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE). Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer?, a detailed solution for Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? has been provided alongside types of Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Consider a random variable x that takes values +1 and -1 with probability 0.5 each. The value of the cumulative distribution function F (x) at x = -1 and + 1 area)0 and 0.5 b)0 and 1c)0.5 and 1d)0.25 and 1Correct answer is option 'C'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
Explore Courses for Electrical Engineering (EE) exam

Top Courses for Electrical Engineering (EE)

Explore Courses
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
10M+ students study on EduRev