ON PYTHON:
a) Write a function named concatTuples(t1, t2) that concatenates
two tuples t1 and t2 and returns the concatenated tuple. Test your
function with t1 = (4, 5, 6) and t2 = (7,)
What happens if t2 = 7? Note the name of the error.
b) Write try-except-else-finally to handle the above tuple
concatenation problem as follows:
If the user inputs an integer instead of a tuple the result of
the concatenation would be an empty tuple. Include an...
On Python:
a) Write a function named concatTuples(t1, t2) that concatenates
two tuples t1 and t2 and returns the concatenated tuple. Test your
function with t1 = (4, 5, 6) and t2 = (7,)
What happens if t2 = 7? Note the name of the error.
b) Write try-except-else-finally to handle the above tuple
concatenation problem as follows:
If the user inputs an integer instead of a tuple the result of
the concatenation would be an empty tuple. Include an...
If T1 and T2 are independent exponential
random variables, find the density function of R=T(2) -
T(1).
This is for the difference of the order statistics not of the
variables, i.e. we are not looking for
T2 - T1. It is implied that they are both
from the same distribution. I know that
fT(t) = λe-λt
fT(1)T(2)(t1,t2) = 2
fT(t1)fT(t2) =
2λ2 e-λt1
e-λt2 , 0 < t1 <
t2 and I need to find fR(r).
From Mathematical Statistics and...
If the moment-generating function of X is M(t) = exp(3 t + 12.5
t2) = e3 t + 12.5 t2.
a. Find the mean and the standard deviation of
X.
Mean =
standard deviation =
b. Find P(4 < X < 16). Round your answer
to 3 decimal places.
c. Find P(4 < X2 < 16). Round
your answer to 3 decimal places.
18. Joint Probability Calculations:
a) What is a joint probability density function?
i. What is an example of a discrete joint probability
function?
ii. What is an example of a continuous joint probability
function?
b) What are marginal density/mass distribution functions? How
can we calculate them from the joint density/mass distribution
functions?
i. Can you calculate the marginals when the joint space is not a
rectangle? (e.g. The space of jpdf[x,y] is 0 < x < y, 0 <
y...
1.Plotting densitiesPlot the probability mass function (pmf) or
probability density function (pdf) for eachof the following
scenarios:(a) Consider abinomialrandom variable,X.i. Plot the pmf
ofX∼Bin(n= 10,p= 0.3).ii. Plot the pmf ofX∼Bin(n= 10,p= 0.7).iii.
Plot the pmf ofX∼Bin(n= 100,p= 0.3).iv. What happens to the shape
of the pmf ofX∼Bin(n,p) whenpgets larger?v. What happens whenngets
larger?(b) Consider ageometricrandom variable,Y.i. Plot the pmf
ofY∼Geom(p= 0.1).ii. Plot the pmf ofY∼Geom(p= 0.5).iii. Plot the
pmf ofY∼Geom(p= 0.8).iv. What happens to the shape of the pmf
ofY∼Geom(p)...
Suppose the installation time in hours for a software on a
laptop has probability density function f(x) = (4/3) (1 −
x3 ), 0 ≤ x ≤ 1.
(a) Find the probability that the software takes between 0.3 and
0.5 hours to be installed on your laptop.
(b) Let X1, . . . , X30 be the
installation times of the software on 30 different laptops. Assume
the installation times are independent. Find the probability that
the average installation time...
Q52 What is a probability density function and how is it
relevant to the determination of probabilities associated with a
continuous random variable? [3 Marks]
DO NOT WRITE THE ANSWER - USE WORD FORMAT.
NO PLAGIARISM ACCEPTED IN THE ANSWER.
1. What is the probability density function?
2. In the Business context, can anyone use an example to show
how the probability density function is applied in the real
world?
Suppose that the distribution of wind velocity, X, is described
by the probability density function f(x) = (x/σ^2)e^-(x^2/ 2(σ^2))
, x ≥ 0. Suppose that for the distribution of wind velocity in
Newcastle, measured in km/hr, σ^2 = 100.
(a) In task 1, you showed that the quantile function for this
distribution is given by: Q(p) = σ (−2 ln(1 − p))^(1/2), 0 ≤ p <
1 Use this quantile function to generate 100,000 random values from
this distribution (when...