# prob April 18, 2012

### 56 terms by dianiline

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### to change any normal distribution to standard normal distribution

subtract m and divide by s

### if you change m

it just moves the curve; z doesn't change

### if you change s

it just scales the curve; z doesn't change

68.27% 34.135%

95.45% 47.725 %

99.73% 49.865%

≈ 2.71828

### conditional distribution

the distribution of one variable given the other

### marginal distribution

distribution of one variable regardless of the value of the other

### multiplication rule

probability of A and B = probability of A times probability of B given A (or vice versa)

probability of A or B = probability of A + probability of B - probability of A and B

1-F(z)

2 F(z) - 1

2.33

1.645

1.28

0.84

0.675

0.55

0.25

0

-0.25

-0.55

-0.675

-0.84

-1.28

-1.645

-2.33

### Theorem 3.6.1 p 220

If you add two independent random variables, the sum is a random variable distributed as the sum of the means, the sum of the standard deviations

### Chi-square distribution

assumes non-negative values only

### t distribution

William Goset; student's t

### F distribution

Fisher distribution; Ronald Fisher; for two independent random variables each with Chi-square distribution p225

### beta distribution a=b=1

The uniform distribution is a special case of the beta distribution where a=b=1.

### beta distribution

non-parametric or distribution-free inference statistical inference where results obtained are general and are applicable to any arbitrary distribution; e.g. % of defective units in a manufacturing process, % of errors made in data entry, and % of fans satisfied with the performance of the team they support

### Chi-square distribution is a special case of the

Gamma distribution where a= n/2 and l=1/2; n is number of degrees of freedom.

p 234

p 236

p238

p 241

p 241

p 242

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