# Uniform distribution

1.

X_1,X_2,...,X_n are independent and uniformly distributed on [0,1]

a. standardize X_1+X_2+...+x_n

b. Give mgf of THE STANDARDIZED (a) sum.

2. Suppose X is normal with mean u and variance sigma^2.

P{u<= X <= u + 1.5 sigma}

https://brainmass.com/statistics/normal-distribution/uniform-distribution-variables-22706

#### Solution Preview

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1. are independent and uniformly distributed on [0,1]

a. standardize

b. Give mgf of THE STANDARDIZED (a) sum.

(a) Solution. Since are independent and uniformly distributed on [0,1], we know that their means and variances are the same. and . So,

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#### Solution Summary

This shows how to standardize the sum of variables and find the MGF.

$2.49