# Question: If the random variable X has the mean and

If the random variable X has the mean µ and the standard deviation s, show that the random variable Z whose values are related to those of X by means of the equation z = x- µ / σ has E(Z) = 0 and var(Z) = 1

A distribution that has the mean 0 and the variance 1 is said to be in standard form, and when we perform the above change of variable, we are said to be standardizing the distribution of X.

A distribution that has the mean 0 and the variance 1 is said to be in standard form, and when we perform the above change of variable, we are said to be standardizing the distribution of X.

## Relevant Questions

If the probability density of X is given by Check whether its mean and its variance exist. Use the inequality of Exercise 4.29 to prove Cheby-shev’s theorem. In exercise P(X ≥ a) ≤ µ / a With reference to Exercise 4.37, find the variance of the random variable by In exercise (a) Expanding the moment-generating function as an infinite series and reading off the necessary coefficients; (b) Using Theorem 4.9. For k random variables X1, X2, . . . , Xk, the values of their joint moment- generating function are given by E(et1X1+ t2X2+ · · · + tkXk) (a) Show for either the discrete case or the continuous case that the partial ...(a) Show that the conditional distribution function of the continuous random variable X, given a< X F b, is given by (b) Differentiate the result of part (a) with respect to x to find the conditional probability density of X ...Post your question