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find the value of k for which the given funcion is a probability density funcion over...

find the value of k for which the given funcion is a probability density funcion over the interval

f(x)= 4x on [1, k]
Math   Statistics-And-Probability   
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Answer #1

X is a continuous random variable, whose probability density function is given by

When   .

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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