## Introduction to mathematical statistics |

### From inside the book

Results 1-3 of 90

Page 22

EXERCISES 1.27. For each of the following, find the constant c so that f(x)

satisfies the conditions of being a p.d.f. of one random variable X. (a) f(x) = c($)x,

x = 1, 2, 3, . . .,

Let f(x) ...

EXERCISES 1.27. For each of the following, find the constant c so that f(x)

satisfies the conditions of being a p.d.f. of one random variable X. (a) f(x) = c($)x,

x = 1, 2, 3, . . .,

**zero elsewhere**. (b) f(x) = cxe~x, 0 < x < co,**zero elsewhere**. 1.28.Let f(x) ...

Page 29

EXERCISES 1.37. Let f(x) be the p.d.f. of a random variable X. Find the

distribution function F(x) of X and sketch its graph if: (a) f(x) = 1, x = 0,

EXERCISES 1.37. Let f(x) be the p.d.f. of a random variable X. Find the

distribution function F(x) of X and sketch its graph if: (a) f(x) = 1, x = 0,

**zero****elsewhere**. (b) f(x) = ^, x = —1, 0, 1,**zero elsewhere**. (c) f(x) = */15, x = l,2, 3, 4, 5,**zero elsewhere**.Page 45

EXERCISES 1.62. Find the mean and variance, if they exist, of each of the

random variables having the indicated probability density functions. 3! /1\3 (a) f(x)

= — , x = 0, 1, 2, 3,

EXERCISES 1.62. Find the mean and variance, if they exist, of each of the

random variables having the indicated probability density functions. 3! /1\3 (a) f(x)

= — , x = 0, 1, 2, 3,

**zero elsewhere**. (b) f(x) = 6x(1 — x), 0 < x < 1,**zero elsewhere**.### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

Accordingly best critical region binomial distribution cent confidence interval Chapter chi-square distribution complete sufficient statistic conditional p.d.f. confidence interval Consider continuous type converges stochastically critical region decision function defined degrees of freedom denote a random discrete type distribution having p.d.f. Equation Example EXERCISES F distribution function of Y1 given H0 is true independent random variables inequality integral joint p.d.f. Let the random Let X1 limiting distribution marginal p.d.f. matrix maximum likelihood moment-generating function mutually stochastically independent noncentral order statistics Poisson distribution positive integer power function Pr X1 probability density functions probability set function quadratic form random experiment random interval random sample random variables X1 reject H0 respectively sample space Show significance level simple hypothesis H0 statistic for 9 statistic Y1 stochastically independent random subset testing H0 theorem type of random unbiased statistic variance a2 X1 and X2 Xn denote zero elsewhere