GATE CE 2014 Set 2 — Question 15
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Engineering Mathematics → Probability → Normal Distribution
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Question
If {x} is a continuous, real valued random variable defined over the interval and its occurrence is defined by the density function given as: where 'a' and 'b' are the statistical attributes of the random variable {x}. The value of the integral is
Correct answer
(B) 0.5
Solution
The given density function is the probability density function (PDF) of a normal distribution with mean and standard deviation . The integral represents the cumulative probability from up to the mean 'a'. Since the normal distribution is symmetric about its mean, the area under the curve to the left of the mean is exactly 0.5. Therefore, the value of the integral is 0.5.
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