Difficult probability question

The probability density of the random variable \(\displaystyle Z\) is given by:

. . . . .\(\displaystyle f(z)\, =\, \begin{cases}kze^{-z^2}&\mbox{ for } z\, >\, 0\\0&\mbox{ for } z\, <\, 0\end{cases}\)

Find \(\displaystyle k\) and draw the graph of this probability density function.

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I know this question might not be all too difficult once I spot something, but I have no idea where to start with this one. Could anyone point me in the right direction please?

I suspect that is a "difficult" probability question only because you have just started studying probability. You know, I hope, that a probability is always between 0 and 1. Since z must be some number, the probability that z is between \(\displaystyle -\infty\) and \(\displaystyle \infty\) is 1.

HallsofIvy said:

I suspect that is a "difficult" probability question only because you have just started studying probability. You know, I hope, that a probability is always between 0 and 1. Since z must be some number, the probability that z is between \(\displaystyle -\infty\) and \(\displaystyle \infty\) is 1.

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I know that the probability is always between 0 and 1, but im still not sure on how to start. Yeah I am new to probability.