Sketch the following probability density function (pdf). Write an equation and sketch the corresponding Cumulative Distribution Function (CDF). Is this random variable discrete or continuous?
Answer the following:
P( V< -0.5 )
P( V < 1.0 )
P( V ≤ 1.0 )
Homework Answers
TOPIC:Sketch of the pmf,cdf and the required
probabilities.
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Sketch the following probability density function (pdf). Write
an equation and sketch the corresponding Cumulative Distribution...
Name: . [20 points] Sketch the following probability density function (pdf). Write an equation and sketch...
Name: . [20 points] Sketch the following probability density function (pdf). Write an equation and sketch the corresponding Cumulative Distribution Function (CDF). Is this random ariable discrete or continuous? y 1 0 otherwise
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given...
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
For a continuous random variable X with the following probability density function (PDF): fX(x) = (...
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)
6. Here is the graph of the probability density function (pdf) fx for a continuous random variabl...
6. Here is the graph of the probability density function (pdf) fx for a continuous random variable X 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 6 10 (a) Sketch the cumulative distribution function (cdf) of X. Label the vertical axis appropriately. (b) Which is larger, P(X 2) or P(X 6)? Explain how you know c) Which is larger, P(1.999 X 2.001) or P(5.999 s X .00)? Explain how you know (d) Which is larger, P(1s X S3) or P(5...
is a continuous random variable with the probability density function (x) = { 4x 0 <=...
is
a continuous random variable with the probability density
function
(x) = {
4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density
function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
Figure out if the following graph can be a "Cumulative Distribution Function (CDF)". If it can,...
Figure out if the following graph can be a "Cumulative Distribution Function (CDF)". If it can, select whether the variable is "Discrete" or "Continuous". (vii) ↑F'(x) Vil 0.5 AC O A. Discrete B.Continuous ° C. Cannot be a CDF
. The average monthly rainfall (AMR) in inches is a random variable with the cumulative distribution...
. The average monthly rainfall (AMR) in inches is a random
variable with the cumulative distribution function (cdf):\
a. Determine the probability that the AMR is less than 1.5
inches.
b. Determine the probability the AMR is between 1.5 and 2
inches.
c. What is the median AMR? d. Determine the equation describing
the probability density function (pdf), f(x)
4 F(x) = .16, otherwise 1.2 1.0 0.8 0.4 0.2 0.0 97.5 98 98.5 99.5 100 100.5
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e...
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
Define the random variable Y = -2X. Determine the cumulative distribution function (CDF) of Y ....
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0,...
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0, xl>3, A1-Show that fr (x) is a valid PDF. B- X is a uniform (-1,3) random variable. Let Y be the output of a clipping circuit with the input X such that Y - 80Q) where χ>0. , B1-Find P(Y-1). B2-Find P(Y 3). B3-Derive and plot the cumulative distribution function (CDF) of the random variable Y, Fy (). B4-What is the probability density function...
Name: . [20 points] Sketch the following probability density function (pdf). Write an equation and sketch the corresponding Cumulative Distribution Function (CDF). Is this random ariable discrete or continuous? y 1 0 otherwise
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
6. Here is the graph of the probability density function (pdf) fx for a continuous random variable X 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 6 10 (a) Sketch the cumulative distribution function (cdf) of X. Label the vertical axis appropriately. (b) Which is larger, P(X 2) or P(X 6)? Explain how you know c) Which is larger, P(1.999 X 2.001) or P(5.999 s X .00)? Explain how you know (d) Which is larger, P(1s X S3) or P(5...
is
a continuous random variable with the probability density
function
(x) = {
4x 0 <= x <= 1/2
{ -4x + 4 1/2 <= x <= 1
What is the equation for the corresponding cumulative density
function (cdf) C(x)?
[Hint: Recall that CDF is defined as C(x) = P(X<=x).]
We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...
Figure out if the following graph can be a "Cumulative Distribution Function (CDF)". If it can, select whether the variable is "Discrete" or "Continuous". (vii) ↑F'(x) Vil 0.5 AC O A. Discrete B.Continuous ° C. Cannot be a CDF
. The average monthly rainfall (AMR) in inches is a random
variable with the cumulative distribution function (cdf):\
a. Determine the probability that the AMR is less than 1.5
inches.
b. Determine the probability the AMR is between 1.5 and 2
inches.
c. What is the median AMR? d. Determine the equation describing
the probability density function (pdf), f(x)
4 F(x) = .16, otherwise 1.2 1.0 0.8 0.4 0.2 0.0 97.5 98 98.5 99.5 100 100.5
Question Let X be a continuous random variable with the following probability density function (pdf) 0.5e fx (x) = { 0.5e-1 x < 0. <>0.. (a) Show that fx (x) is a valid pdf. (b) Find the cumulative distribution function Fx (.x). (e) Find F='(X). (d) Write an algorithm to generate a sample of size 1000 from the distribution of X using the inverse-transform method. Be as precise as possible.
Define the random variable Y = -2X. Determine the cumulative
distribution function (CDF) of Y . Make sure to completely specify
this function. Explain.
Consider a random variable X with the following probability density function (PDF): s 2+2 if –2 < x < 2, fx(x) = { 0 otherwise. This random variable X is used in parts a, b, and c of this problem.
Q1) A-Random variable X has the following Probability Density Function (PDF) fr(x)= 부.lel s 3. (0, xl>3, A1-Show that fr (x) is a valid PDF. B- X is a uniform (-1,3) random variable. Let Y be the output of a clipping circuit with the input X such that Y - 80Q) where χ>0. , B1-Find P(Y-1). B2-Find P(Y 3). B3-Derive and plot the cumulative distribution function (CDF) of the random variable Y, Fy (). B4-What is the probability density function...
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