Let X be a random variable with density functionfX (x) = k1 + x2 , −∞ < x < ∞.Determine k and the distribution function
Question
Solution 1
To find the value of k such that the function f is a probability density function, we need to ensure that the integral of f from -∞ to ∞ is equal to 1, because the total probability must be 1.
The function f is non-zero for all real numbers, so we need to integrate from -∞ to ∞:
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