## Introduction to Mathematical Statistics |

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Page 22

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) ... Let f(x) = x/15, r = 1, 2, 3, 4, 5, zero

elsewhere, be the p.d.f. of X. Find

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) ... Let f(x) = x/15, r = 1, 2, 3, 4, 5, zero

elsewhere, be the p.d.f. of X. Find

**Pr**[**X**= 1 or 2), Pr[4 × X & #), and Pr[1 < X > 2].Page 25

In listing these properties, we shall not restrict X to be a random variable of the

discrete or continuous type. (a) 0 < F(x) → 1 because 0 <

a nondecreasing function of ar. For, if a.' < r", then {z; a s ar") = {ar; a > a.'} U {x; ac'

...

In listing these properties, we shall not restrict X to be a random variable of the

discrete or continuous type. (a) 0 < F(x) → 1 because 0 <

**Pr**(**X**= x) < 1. (b) F(x) isa nondecreasing function of ar. For, if a.' < r", then {z; a s ar") = {ar; a > a.'} U {x; ac'

...

Page 94

is said to have a chi-square distribution; and any f(x) of this form is called a chi-

square p.d.f. The mean and the ... If the random variable X is x*(r), then, with c1 <

ca, we have Pr (c1 < X > ca) =

is said to have a chi-square distribution; and any f(x) of this form is called a chi-

square p.d.f. The mean and the ... If the random variable X is x*(r), then, with c1 <

ca, we have Pr (c1 < X > ca) =

**Pr**(**X**= ca) —**Pr**(**X**= ci), since**Pr**(**X**= ca) = 0.### What people are saying - Write a review

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accept accordance Accordingly alternative approximately assume called cent Chapter complete compute conditional confidence interval Consider constant continuous type critical region decision defined definition degrees of freedom denote a random depend determine discrete type distribution function equal Equation event Example EXERCISES exists expected fact given Hence inequality integral interval joint p.d.f. Let X1 likelihood marginal matrix maximum mean moment-generating function mutually stochastically independent normal distribution Note observed order statistics outcome parameter Pr(X probability density functions problem proof prove random experiment random interval random sample random variable ratio reject respectively result sample space Show significance level simple hypothesis ſº stochastically independent sufficient statistic symmetric matrix Table theorem transformation true unknown variance write X1 and X2 zero elsewhere