## Introduction to Mathematical Statistics |

### From inside the book

Results 1-3 of 83

Page 139

Some illustrative examples of

be a discrete type of random variable having p.d.f. f(z) - 1, 2 = C, = 0 elsewhere.

This simplest of discrete-type distributions, which has all the probability at one ...

Some illustrative examples of

**distribution functions**now follow. ExAMPLE 1. Let Xbe a discrete type of random variable having p.d.f. f(z) - 1, 2 = C, = 0 elsewhere.

This simplest of discrete-type distributions, which has all the probability at one ...

Page 140

If X has the p.d. f. f(z) = z/15, 2 = 1, 2, 3, 4, 5, zero elsewhere, determine the

2a:”, 0 < x < 3%, = 1 — 2(1 — 2)”, 3% s r < 1, = 1, 1 < z. Compute (a) Pr(9% X 3

%) and ...

If X has the p.d. f. f(z) = z/15, 2 = 1, 2, 3, 4, 5, zero elsewhere, determine the

**distribution function**F(z) of X. 7.3. Given the**distribution function**F(x) = 0, x < 0, =2a:”, 0 < x < 3%, = 1 — 2(1 — 2)”, 3% s r < 1, = 1, 1 < z. Compute (a) Pr(9% X 3

%) and ...

Page 142

This may suggest that X has no limiting distribution. However, the

1, a > 2. Since F(x) = 0, a 3 2, = 1, 2 × 2, is a

) ...

This may suggest that X has no limiting distribution. However, the

**distribution****function**of X is Fn(z) = 0, 2 < 2+}, 1 - 1, 2 > 2 + m' and lim Fn(x) = 0, a 3 2, n-)-co =1, a > 2. Since F(x) = 0, a 3 2, = 1, 2 × 2, is a

**distribution function**, and since o Fn(z) ...

### 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 chi-square distribution composite hypothesis conditional p.d.f. confidence interval Consider continuous type degrees of freedom denote a random discrete type distribution function distribution having p.d.f. distribution with mean ExAMPLE Exercises f(zi function F(z hypothesis H1 independent random variables integral Jacobian joint p.d.f. joint sufficient statistics Let the random Let X1 limiting distribution marginal p.d.f. moment-generating function mutually stochastically independent Mx(t My(t normal distribution n(z null hypothesis null simple hypothesis one-to-one transformation order statistics p.d.f. of Yi Poisson distribution positive integer Pr(a Pr(X Pr(Y probability density functions quadratic form random experiment random interval random sample random variables X1 respectively ſ ſ sample space Show significance level ſº stochastically independent random subset sufficient statistic Yi theorem tion type of random unbiased statistic values X1 and X2 Xn denote zero elsewhere