Question
In: Statistics and Probability
X is a random variable for losses. X follows a beta distribution with θ = 1000,...
X is a random variable for losses. X follows a beta distribution with θ = 1000, a = 2, and b = 1. Calculate TVaR0.90(X)
Solutions
orchestra answered 2 years agoRelated Solutions
For a random variable X with a Cauchy distribution with θ = 0 , so that...
For a random variable X with a Cauchy distribution with θ = 0 ,
so that
f(x) =(1/ π)/( 1 + x^2) for -∞ < x < ∞
(a) Show that the expected value of the random variable X does not
exist.
(b) Show that the variance of the random variable X does not
exist.
(c) Show that a Cauchy random variable does not have finite moments
of order greater than or equal to one.
Let x be a continuous random variable that follows a distribution skewed to the left with...
Let x be a continuous random variable that follows a
distribution skewed to the left with ?= 92 and ?=15. Assuming n/N
<= .05, find the probability that the sample mean, x bar, for a
random sample of 62 taken from this population will be (ROUND
ANSWERS TO FOUR DECIMAL PLACES):
a) less than 81.5
P(less that 81.5)=
b) greater than 89.7
P(greater than 89.7)=
Please show your work.
The random variable X follows a normal distribution with a mean of 10 and a standard...
The random variable X follows a normal distribution with a mean
of 10 and a standard deviation of 3.
1.
What is P(7≤X≤13)? Include 4 decimal places in your answer.
2.
What is the value of k such that P(X>k)=0.43? Include 2
decimal places in your answer.
The random variable X has an Exponential distribution with parameter beta= 5. The P(X > 18|X...
The random variable X has an Exponential distribution with
parameter beta= 5. The
P(X > 18|X > 12) is equal to
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
If a random variable X has a beta distribution, its probability density function is fX (x)...
If a random variable X has a beta distribution, its probability
density function is
fX (x) = 1 xα−1(1 − x)β−1 B(α,β)
for x between 0 and 1 inclusive. The pdf is zero outside of
[0,1]. The B() in the denominator is the beta function, given by
beta(a,b) in R.
Write your own version of dbeta() using the beta pdf formula
given above. Call your function mydbeta(). Your function can be
simpler than dbeta(): use only three arguments (x, shape1,...
A random variable X follows the continuous uniform distribution with a lower bound of ?8 and...
A random variable X follows the continuous uniform
distribution with a lower bound of ?8 and an upper bound of 11.
a.
What is the height of the density function
f(x)? (Round your answer to 4 decimal
places.)
f(x)
b.
What are the mean and the standard deviation for the
distribution? (Round your answers to 2 decimal
places.)
Mean
Standard
deviation
c.
Calculate P(X ? ?6). (Round
intermediate calculations to 4 decimal places and final answer to...
A random variable X follows a uniform distribution on the interval from 0 to 20. This...
A random variable X follows a uniform distribution on the
interval from 0 to 20. This distribution has a mean of 10 and a
standard deviation of 5.27. We take a random sample of 50
individuals from this distribution. What is the approximate
probability that the sample mean is less than 9.5
1) Let x be a continuous random variable that follows a normal distribution with a mean...
1) Let x be a continuous random variable that
follows a normal distribution with a mean of 321 and a standard
deviation of 41.
(a) Find the value of x > 321 so
that the area under the normal curve from 321 to x is 0.2224.
Round your answer to the nearest integer.
The value of x is_______
(b) Find the value of x so that the area under
the normal curve to the right of x is 0.3745.
Round...
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