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Question 1

Continuous normal distribution

Answer 1

is described by a lower limit, a, and an upper limit, b. These limits serve as the parameters of the distribution.

Question 2

in Continuous normal distribution, the probability of any outcome or range of outcomes outside the limits a, and b is ____

Answer 2

0

Question 3

give the probability of random variables being outside the parameters of a continuous distribution

Answer 3

P(Xb) = 0

Question 4

P(X ≥ x) is the same as P(X ﹥ x) for a continuous distribution because P(X = x) equals ____.

Answer 4

1. zero

Question 5

in a continuous distribution, the probability that a random variable, X will take a value that falls between x_1 and x_2 within the range a to b is…

Answer 5

the proportion of the area from x_1 to x_2 divided by the area from a to b –>
P(x1≤X≤x2) = (x_2 - x_1) / b-a

Question 6

normal distribution shape is..

Answer 6

• ## bell shaped

Question 7

Normal distribution is completely described by its mean (μ) and variance (σ2). The distribution is stated as X ∼ N (μ,σ2), which is read as ….

Answer 7

• the random variable X follows the normal distribution with mean, μ and variance, σ2.

Question 8

The normal distribution has a skewness of 0, which means that it is ______ about its mean. P(X≤mean)=P(X≥mean)=.5

Answer 8

1. symmetric

Question 9

normal distribution mean, median, modes, are…

Answer 9

all the same, betch

Question 10

whats the kurtosis of standard normal distribution? whats the excess kurtosis?

Answer 10

3 and excess = 0

Question 11

if the returns on each stock in a portfolio is a linear distribution, the portfolio has a ________

Answer 11

linear dist as well

Question 12

describe probability of a random variable lying in ranges further away from the mean in a normal distribution..

Answer 12

probability gets lower and lower the further away from the mean, but never reaches zero

Question 13

univariate distribution..

Answer 13

describe the distribution of a single random variable – up to this point, we have only dealt with this shit

Question 14

multivariate distribution

Answer 14

specify probabilities associated with a group of random variables taking into account the interrelationships that may exist between them.

Question 15

multivariate example?

Answer 15

a linear combination of normally distributed variables al put together in a portfolio would still have a normal distribution – this is said to have a multivariate normal distribution

Question 16

the need to know _____ is what differentiates multivariate normal distributions from univariate normal distributions.

Answer 16

1. correlations

Question 17

A multivariate normal distribution for the return on a portfolio with n stocks is completely defined by the following three parameters:

Answer 17

• The mean returns on all the n individual stocks (μ_1,μ_2,…..,μ_n)
• The variances of returns of all n individual stocks (σ_1^2,σ_2^2,…..,σ_n^2)
• The return correlations between each possible pair of stocks. There will be n(n-1)/2 pairwise correlations in total. (Correlation is a measure of the strength of the linear relationship between 2 variables).3

Question 18

If we are studying returns on a portfolio consisting of 4 assets, we will use __ means, __ variances, and the ___ correlations to describe the multivariate distribution.

Answer 18

1. 4
2. 4
3. 6

Question 19

A confidence interval represents …

Answer 19

the range of values within which a certain population parameter is expected to lie in a specified percentage of the time.

Question 20

in practice we do not know the population parameters, so we…

Answer 20

estimate them

Question 21

the three confidence intervals that we encounter most frequently are

Answer 21

90%
95%
99%

Question 22

for: 90%
95%
99%, what are their respective standard deviations from the mean?

Answer 22

90% = +or - 1.65s

95% = + or - 1.96s

99% = + or - 2.58s