Name: . [20 points] Sketch the following probability density function (pdf). Write an equation and sketch...
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 )
fv(v)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)
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)
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...
1. 20 points Let X be a random variable with the following probability density function: f(x)--e+1" with ? > 0, ? > 0, constants x > ?, (a) 5 points Find the value of constant c that makes f(x) a valid probability mass function. (b) 5 points Find the cumulative distribution function (CDF) of X.
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.
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...
15. (10 points) A. Draw a graph of the probability distribution function (PDF) for the uniform distribution that is defined to be non-zero and constant between 1 and 10. Label the x and y-axes for the graph. (3 points) B. On the same graph draw the cumulative distribution function (CDF) for the uniform distribution. Clearly identify each line (PDF or CDF) in the graph. (3 points) C. In words, express the mathematical relationship that exists between any CDF and the...
Answer True or False for the following questions: 1. The probability density function (pdf) is used to describe probabilities for continuous random variables. 2. The cumulative distribution function (cdf) gives the probability as an area. 3. The amount of time (beginning now) until an earthquake occurs has an uniform distribution 4. Normal distributions are commonly used in calculations of product reliability, or the length of time a product lasts. 6. The exponential distribution has the decay parameter, which says that...
Please solve part e! Priority!
1. (10 points) Let a random variable Y have probability density f(), 0 :otherwise (a) (2 points) Find the normalization constant c (b) (2 points) Write the expression for the cumulative distribution function (CDF) (c) (2 points) Find ElY] (d) (2 points) Find Var(Y)