Quantitative Methods IV

Question 1

Binomial distribution

Answer 1

Success and failure, where prob is constant for each trial

Question 2

Binomial expected value

Answer 2

E(x) = N * P

Number of trials * probability of success

Question 3

Binomial variance

Answer 3

N * P * (1-P)

Question 4

Continuous uniform distribution

Answer 4

Prob of outcome = % of range

I.e. range = 2 to 12, prob of 4 to 8 = (8-4) / (12-2)

Question 5

Normal distribution

Answer 5

mean = mode = median
Kurtosis = 3
Skewness = 0

Question 6

Multivariate distributions
Mean
Variance
Correlation

Answer 6

N means

N variances

0.5N(n-1) pairs of correlation

Question 7

Confidence intervals for normal distribution

Answer 7

90% = -1.65s to 1.65s
95% = -1.96s to 1.96s
99% = -2.58s to 2.58s

Question 8

Z-score

Answer 8

(sample mean - hypothesized mean) / standard error

How many stdevs away from the mean you are
Standardized so mean = 0, stdev = 1

Question 9

Lognormal distributions

Answer 9

e^x

Skewed to the right and bounded by zero, useful with non negative asset prices

Question 10

Compounding with continuous periods

Effective annual rate

Answer 10

e^r - 1

R = return

Question 11

Compounding with continuos periods

Convert effective rate to stated rate

Answer 11

Ln(effective rate + 1)

Question 12

Stratified random sample

Answer 12

Classification system to separate into subgroups and then take samples based on size relative to population.

Guaranteed to sample from each stratum, not true of simple random sample.

Question 13

Central limit theorem

Answer 13

Sample distribution approaches normal as sample grows

Variance of distribution of sample means = variance / n

Question 14

Standard error of sample mean

Answer 14

standard deviation / sqrt(N)

Question 15

Level of significance

Answer 15

5% significance = 95% confidence

Question 16

T distribution properties

Answer 16

One-tailed probabilities

Degrees of freedom = n - 1

Question 17

Normal, unknown variance, small or large sample

Answer 17

T-statistic

Question 18

Non-normal, regardless of var, small sample

Answer 18

Cannot use T or Z

Question 19

Normal, known variance, small or large

Answer 19

Z-statistic

Question 20

Non-normal, known var, large sample

Answer 20

Z-Statistic