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Let X be a Gaussian random variable mean 0 and variance σ2. Let Y = max(X, 0) where max(a,b) is the maximum of a and b. The median of Y is:
Correct answer is '0'. Can you explain this answer?
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Most Upvoted Answer
Let X be a Gaussian random variable mean 0 and variance σ2. Let ...
Given,
'X' is Gaussian random variable,
= X ∼ N(0, σ2) for − ∞ < x < ∞
Since median is positional average.
Therefore, median of Y is '0'.
Hence, the correct answer is 0.
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Let X be a Gaussian random variable mean 0 and variance σ2. Let ...
1. The probability density function (PDF) of a Gaussian random variable with mean 0 and variance 1 is given by:
f(x) = (1/sqrt(2*pi))*exp(-x^2/2)
2. The cumulative distribution function (CDF) of the Gaussian random variable can be defined as:
F(x) = ∫[−∞, x] f(t) dt
3. The mean (or expected value) of a Gaussian random variable with mean 0 and variance 1 is 0.
4. The variance of a Gaussian random variable with mean 0 and variance 1 is 1.
5. The standard deviation of a Gaussian random variable with mean 0 and variance 1 is also 1.
6. The moment generating function (MGF) of a Gaussian random variable with mean 0 and variance 1 is:
M(t) = exp(t^2/2)
7. The characteristic function of a Gaussian random variable with mean 0 and variance 1 is:
φ(t) = exp(-t^2/2)
f(x) = (1/sqrt(2*pi))*exp(-x^2/2)
2. The cumulative distribution function (CDF) of the Gaussian random variable can be defined as:
F(x) = ∫[−∞, x] f(t) dt
3. The mean (or expected value) of a Gaussian random variable with mean 0 and variance 1 is 0.
4. The variance of a Gaussian random variable with mean 0 and variance 1 is 1.
5. The standard deviation of a Gaussian random variable with mean 0 and variance 1 is also 1.
6. The moment generating function (MGF) of a Gaussian random variable with mean 0 and variance 1 is:
M(t) = exp(t^2/2)
7. The characteristic function of a Gaussian random variable with mean 0 and variance 1 is:
φ(t) = exp(-t^2/2)
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Let X be a Gaussian random variable mean 0 and variance σ2. Let Y = max(X, 0) where max(a,b) is the maximum of a and b. The median of Y is:Correct answer is '0'. Can you explain this answer?
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