Hi. I got stuck in this problem, wondering if anyone can help?
Given that P(X<=M) = P(X>M) = 1/2. For random variable X with f(x) = 1/sqrt(2π)σ * e^-((x-m)^2)/(2σ^2), I am asked to find the median.
To find the median (which is equals to expected value(?)), I think I need to integrate x*f(x), but what is the range going to be? It look very difficult to integrate. I was given a hint: I was told to think of the curve as in symmetric, so that the area under the left half of the curve is equal to the other half of curve. And in such case, median=0. But I still don't get how that is useful for solving this problem. Any input will be appreciated! Thanks.
Given that P(X<=M) = P(X>M) = 1/2. For random variable X with f(x) = 1/sqrt(2π)σ * e^-((x-m)^2)/(2σ^2), I am asked to find the median.
To find the median (which is equals to expected value(?)), I think I need to integrate x*f(x), but what is the range going to be? It look very difficult to integrate. I was given a hint: I was told to think of the curve as in symmetric, so that the area under the left half of the curve is equal to the other half of curve. And in such case, median=0. But I still don't get how that is useful for solving this problem. Any input will be appreciated! Thanks.
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The Normal Distribution is symmetric, so the Mean = Median.
You'll be integrating from -infinity to +infinity
You'll be integrating from -infinity to +infinity