The random variables X and Y have the following probability density function (pdf).
Conditional probability density function is
f(xly) = ax/y^2 , 0<x<y, 0<y<1
=0 , o/w
marginal density finction is
f(y) = by^4 ,0<y<1
= 0, o/w
At this time, find the constant a and b values to be the probability density function, and then indicate whether the random variables X and Y are independent, and if not, indicate whether they are positive or inverse.
In: Statistics and Probability
Expected Returns: Discrete Distribution
The market and Stock J have the following probability distributions:
| Probability | rM | rJ |
| 0.3 | 14% | 18% |
| 0.4 | 9 | 7 |
| 0.3 | 19 | 12 |
In: Economics
What is a probability space (aka probability model, aka formal statistical model)? (b) Give a concrete example (be explicit, and avoid using just words if possible).
In: Statistics and Probability
Probability:
Given that there were 500 individuals studied:
Find the probability that:
p(S/V) person was sick, given that the person was vacationing.
| working | vactioning | |
| sick | 170 | 85 |
| healthy | 80 | 165 |
|
0.27 |
||
|
0.34 |
||
|
0.55 |
||
|
0.92 |
In: Statistics and Probability
In: Statistics and Probability
17#11
Let us suppose that a certain probability instructor manages, with probability 1, to write exams that have mean 60 and standard deviation 12. The instructor is teaching two classes, one of size 64 and the other of size 36, and is about to give an exam to both classes.
(a) Approximate the probability that the
average test score in the class of size 64 exceeds 65.
Probability ≈≈
(b) Repeat part (a) for the class of size
36.
Probability ≈≈
(c) Approximate the probability that the
average test score in the larger class exceeds that of the other by
more than 2 points.
Probability ≈≈
(d) Approximate the probability that the
average test score in the smaller class exceeds that in the other
by more than 2 points.
Probability ≈
In: Statistics and Probability
In: Finance
Identify and describe two types of non-probability sampling methods and two types of probability sampling methods
In: Statistics and Probability
Simulating a conditional probability using R.
Simulating the conditional probability P(A|B) requires repeated
simulation of
the underlying random experiment, but restricting to trials in
which B occurs.
Suppose 3 dice are tossed and we want to find the probability of
the first die is 4 given that the sum is 10.
Modify the script ConditionalDice.R (you can find the R script file
from Modules on this Canvas site) to find
P(First die is 4 | Sum is 10)
Hint: the exact answer is: 5/27.
### R: Simulating a conditional probability
#Simulating the conditional probability P(A|B) requires repeated
simulation of
#the underlying random experiment, but restricting to trials in
which B occurs.
### ConditionalDice.R
### Suppoese we roll 2 dice and want to find
### P(First die is 2 | Sum is 7)
### We know that answer is: 1/6.
### In this case, we repeatly toss two dice, but the only data
that we keep
### are those pairs whose sum is 7.
n <- 60000
ctr <- 0
# ctr is the counter for the rolls when the sum is 7
simlist <- replicate(n, 0) ## Initialize list with 0's
while (ctr < n)
{
trial <- sample(1:6, 2, replace=TRUE) ## Roll 2
dice
if (sum(trial) == 7) ### Check if sum is 7
### If not, skip through and roll again
### If 7, check if first die is a 2
{
success <- if (trial[1] == 2) 1 else 0
ctr <- ctr + 1
simlist[ctr] <- success
### simlist records successes and failures only
for
### dice rolls that sum to 7
}
}
### Simulated result
simlist
mean(simlist)
In: Computer Science
The market and Stock J have the following probability distributions:
|
Probability |
rM |
rJ |
|
0.3 |
16% |
22% |
|
0.4 |
8 |
7 |
|
0.3 |
20 |
12 |
a. Calculate the expected rate of return for the market. Round your answer to two decimal places.
a1. Calculate the expected rate of return for Stock J. Round your answer to two decimal place
b. Calculate the standard deviation for the market. Do not round intermediate calculations. Round your answer to two decimal places.
b2. Calculate the standard deviation for Stock J. Do not round intermediate calculations. Round your answer to two decimal places
In: Finance