X is a continuous random variable, whose probability density function is given by
We have to find the value of k.
Now, we know that a probability density function, when integrated over the whole range of the random variable, results in 1.
So, by this property,
So, approximately, k is 1.2247.
Thus, the value of k, for which the given function is a probability density function, is square root of 1.5, ie. 1.2247 approximately.
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