whitedragonxx said:Homework Statement
Let Z follow a standard normal distribution. Compute E(Z^3) and E(Z^4)
Homework Equations
I know that mu is 0 and sigma is 1. And f(z) = e^(-z^2/2)/sqrt(2pi)
The Attempt at a Solution
I tried to take the integral of ∫Z^3 * f(z) from the integral from -∞ to ∞
and did the same for E(Z^4) where the Z^3 is replaced by Z^4, but I don't know if I am doing the problem right or wrong.
The standard normal distribution is a type of probability distribution that is commonly used in statistics. It is also known as the Gaussian distribution or the bell curve. It is a symmetrical distribution with a mean of 0 and a standard deviation of 1.
The standard normal distribution is unique because it has a mean of 0 and a standard deviation of 1. This allows for easy comparison and calculation of probabilities. Other distributions may have different means and standard deviations, making them more difficult to compare and analyze.
The standard normal distribution is a continuous distribution, meaning that it can take on any value within a certain range. It is also symmetrical, with the mean, median, and mode all being equal. Additionally, about 68% of the data falls within one standard deviation of the mean, and about 95% falls within two standard deviations.
The standard normal distribution is used to calculate probabilities and make statistical inferences. It is often used in hypothesis testing, confidence intervals, and regression analysis. It is also used to standardize data, making it easier to compare different sets of data.
The z-score is a measure of how many standard deviations a data point is above or below the mean of a distribution. In the case of the standard normal distribution, the z-score is equivalent to the number of standard deviations a data point is from the mean. This allows for easy calculation of probabilities and comparisons across different distributions.