Question
In: Statistics and Probability
A continuous probability density function (PDF) f ( X ) describes the distribution of continuous random...
A continuous probability density function (PDF) f ( X ) describes the distribution of continuous random variable X . Explain in words, and words only, this property: P ( x a < X < x b ) = P ( x a ≤ X ≤ x b )
Solutions
Expert Solution
For any continuous random variable the probability that x=a or x=b is zero.There is no defined probability for continuous variables at any given fixed point. So, equality sign does not make any difference in the probabilities.
Therefore both given probabilities are same.
orchestra answered 2 years agoRelated Solutions
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
Consider a continuous random variable X with the probability density function f X ( x )...
Consider a continuous random variable X with the probability
density function f X ( x ) = x/C , 3 ≤ x ≤ 7, zero elsewhere.
Consider Y = g( X ) = 100/(x^2+1). Use cdf approach to find the cdf
of Y, FY(y). Hint: F Y ( y ) = P( Y <y ) = P( g( X ) <y )
=
If a continuous random process has a probability density function f(x) = a + bx, for...
If a continuous random process has a probability density
function f(x) = a + bx, for 0 < x < 5, where a and b are
constants, and P(X > 3) = 0.3 Determine:
The values of a and b.
The cumulative distribution function F(x)
P(X < 2)
P(2 < X < 4)
If a continuous random process has a probability density function f(x) = a + bx, for...
If a continuous random process has a probability density
function f(x) = a + bx, for 0 < x < 5, where a and b are
constants, and P(X > 3) = 0.3 Determine:
The values of a and b.
The cumulative distribution function F(x)
P(X < 2)
P(2 < X < 4)
2 Consider the probability density function (p.d.f) of a continuous random variable X: f(x) = (...
2 Consider the probability density function (p.d.f) of a
continuous random variable X: f(x) = ( k x3 , 0 < x < 1, 0,
elsewhere, where k is a constant. (a) Find k. (b) Compute the
cumulative distribution function F(x) of X. (c) Evaluate P(0.1 <
X < 0.8). (d) Compute µX = E(X) and σX.
Assume that a continuous random variable has a following probability density function: f ( x )...
Assume that a continuous random variable has a following
probability density function:
f ( x ) = { 1 10 x 4 2 ≤ x ≤ 2.414 0 o t h e r w i s e
Use this information and answer questions 3a to 3g.
Question a: Which of the
following is a valid cumulative density function for the defined
region ( 2 ≤ x ≤ 2.414)?
A.F x ( x ) = 1 50 x 5 −...
The random variable Y has an exponential distribution with probability density function (pdf) as follows: f(y)...
The random variable Y has an exponential distribution with
probability density function (pdf)
as follows:
f(y) = λe−λy, y >0
= 0, otherwise
(i) Showing your workings, find P (Y > s|Y > t), for s ≥
t. [3]
(ii) Derive an expression for the conditional pdf of Y ,
conditional on that Y ≤ 200. [3]
N(t) is a Poisson process with rate λ
(iii) Find an expression for the Cumulative Distribution
Function (CDF) of the waiting time until...
The random variables X and Y have the following probability density function (pdf). Conditional probability density...
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.
Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...
Consider a continuous random vector (Y, X) with joint
probability density function
f(x, y) = 1
for 0 < x < 1, x < y < x + 1.
What is the marginal density of X and Y? Use this to compute
Var(X) and Var(Y)
Compute the expectation E[XY]
Use the previous results to compute the correlation Corr (Y,
X)
Compute the third moment of Y, i.e., E[Y3]
Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...
Consider a continuous random vector (Y, X) with joint
probability density function f(x, y) = 1 for 0 < x < 1, x
< y < x + 1.
A. What is the marginal density of X and Y ? Use this to compute
Var(X) and Var(Y).
B. Compute the expectation E[XY]
C. Use the previous results to compute the correlation Corr(Y,
X).
D. Compute the third moment of Y , i.e., E[Y3].
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- 1.) Think back to August 6, 1945. The United States has just dropped an atomic weapon...
- Carry out the equipment and operating procedures between injection molding of thermoplastics and injection molding of...
- The cumulative timing approach was used to time a job and its elements. Use the following...
- absorption refection scattering refraction and diffraction can all have an impact on RF signal strength. Identify...
- This is my code I need to complete it? //The code package arraylists; import java.util.ArrayList; import...
- Organization management function at Tesla, and how can they improve the structure
- A company orders every 8 weeks. 52 weeks/8 weeks per order = 6.5 orders per year....
ADVERTISEMENT