Question

1. Let fX(x;μ,σ2) denote the probability density function of a normally distributed variable X with mean...

1. Let fX(x;μ,σ2) denote the probability density function of a normally distributed variable X with mean μ and variance σ2.

a. What value of x maximizes this function?

b. What is the maximum value of fX(x;μ,σ2)?

Math   Statistics-And-Probability   
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Answer #1

The probability density function of a normally distributed random variable X with mean and variance is

a) It is clear that as the values of x increases or decreases the value of decreases. The maximum value occurs at

As at .

So, the required value of x which maximizes this function is

b) Put in we get the required maximum value as

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