Exercises due Oct 30, 2024 17:29 IST
Exercise: Correlation coefficient
1 point possible (graded)
It is known that for a standard normal random variable \( X \), we have \( \mathbf{E}\left[X^{3}\right]=0, \mathbf{E}\left[X^{4}\right]=3 \), \( \mathbf{E}\left[X^{5}\right]=0, \mathbf{E}\left[X^{6}\right]=15 \). Find the correlation coefficient between \( X \) and \( X^{3} \). Enter your answer as a number.
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