Question
In: Computer Science
A probability distribution function P(x) for a random variable X is defined by P(x) = P...
A probability distribution function P(x) for a random variable X is defined by P(x) = P r{X ≤ x}. Suppose that we draw a list of n random variables X1, X2, X3 · · · Xn from a continuous probability distribution function P that is computable in O(1) time. Give an algorithm that sorts these numbers in linear average case time.
Solutions
venereology answered 1 year agoRelated Solutions
1. The probability mass function of a discrete random variable X is defined as p(x) =...
1. The probability mass function of a discrete random variable X
is defined as p(x) = ax for x = 1, 2, 4, 8 (p(x) =0 for all other
values) then the value of a is?
2. Let X be a discrete random variable with Var(X) =6.0 and
E(X2) = 17.00. Then: E(X) = ?
3. If X is a binomial random variable with parameters n and p,
i.e. X ~ b(x; n, p), then the expected value of X...
Let X be a random variable with the following probability distribution: Value x of X P(X=x) ...
Let X be a random variable with the following probability
distribution:
Value x of X P(X=x)
20 0.35
30 0.10
40 0.25
50 0.30
Find the expectation E (X) and variance Var (X) of X. (If
necessary, consult a list of formulas.)
E (x) = ?
Var (X) = ?
Considering X a continuous random variable defined by the distribution function f(x) = 0 if x<1...
Considering X a continuous random variable defined by the
distribution function
f(x) = 0 if x<1
-k +k/x if 1<= x < 2
1 if 2<x
Find k.
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,...
Question 1: Given the following probability distribution for a random variable X: x P(X=x) -2 0.30...
Question 1:
Given the following probability distribution for a random variable
X: x P(X=x)
-2
0.30
-1
0.15
0
0.20
1
0.20
2
0.15
a) Explain two reasons why the above distribution is a valid
probability distribution.
b) Calculate μX and σX.
c) Determine the cdf(X), and write it as an additional column in
the table.
d) Calculate P(−1<X≤3) .
e) Draw a histogram that represents the probability distribution of
X.
Let the continuous random variable X have probability density function f(x) and cumulative distribution function F(x)....
Let the continuous random variable X have probability density
function f(x) and cumulative distribution function F(x). Explain
the following issues using diagram (Graphs)
a) Relationship between f(x) and F(x) for a continuous
variable,
b) explaining how a uniform random variable can be used to
simulate X via the cumulative distribution function of X, or
c) explaining the effect of transformation on a discrete and/or
continuous random variable
A discrete random variable named X has the following pmf (probability mass function): X P(x) 1...
A discrete random variable named X has the following
pmf (probability mass function):
X
P(x)
1
0.6
3
0.2
7
0.1
11
0.1
17a) Find P(X>6)
17b) What is the probability two independent observations of X
will both equal 1?
17c) Find the population mean also known as E(X)= the expected
value of
17d) Find the population variance of X with both the “regular”
formula and “convenient”
formula
Make a table and show your work. You should get the same...
The velocity of a particle in a gas is a random variable X with probability distribution...
The velocity of a particle in a gas is a random variable
X with probability distribution
fX (x) =
32 x2 e−4x ,
x>0. The kinetic energy of the particle is (1/2)
mX 2. Suppose that the mass of the particle is
64 yg. Find the probability distribution of Y. (Do not
convert any units.) Please explain steps. I do not understand how
to solve this kind of question. Thank you! :)
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