Let be the random variable X with distributionfunction given by:Fx (x) = -01exFind the density function of X.b) findP[+SX51<42x ≤00 < x < 1x ≥1c) Find the expectation of X.d) Find the variance of Xe) Find the standard deviation of X.

As per our guidelines I can solve only first three subparts. Kindly post the remaining subparts…

Answered: Let be the random variable X with…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

Find the moment-generating function of the contin-uous random variable X whose probability density is given by f(x) =1 for 0 < x < 10 elsewhere and use it to find μ1,μ2, and σ2.
Let X be the amount of premium gasoline (in 1000 gallons) that a service station has in its tanks at the beginning of a day, and Y the amount that the service station sells during that day. If the joint density of X and Y is given byf (x, y) = 1/200, for 0 <y <x <20, use the distribution function techniques to find the probability density of the amount that the service station has left in its tanks at the end of the day
Find the joint probability density of the two randomvariables X and Y whose joint distribution function isgiven byF(x, y) = 1 − e−x − e−y + e−x−y for x > 0, y > 00 elsewhere
Let X denote the reaction time, in seconds, to a certain stimulus and Y denote the temperature (◦F) at which a certain reaction starts to take place. Suppose that two random variables X and Y have the joint density
Suppose that two continuous random variables X and Y have joint probability density function fxy = A( ex+y + e2x+y) , 1 ≤ x ≤ 2 ,0≤ y≤3 0 elsewhere a. P ( 3/2 ≤ X ≤ 2, 1 ≤ Y ≤ 2) b. Are the random variables X and Y independent? c. find the conditional density X given Y = 0
Determine the conditional probability distribution of Y given that X = 1. Where the jointprobability density function is given by f(x,y)=1/64xy for 0 < x < 4 and 0 < y < 4.
Let X and Y be a pair of continuous random variables with a joint density fx,y(x,y). Assume that fx,y(x,y) = cxy for x greater than or equal to 0, y greater than or equal to 0, and x + y less than or equal to 1. Here c is a constant. Assume that fx,y(x,y) is 0 elsewhere. What is the constant c equal to? With the value of c, what is E[XY]?
Suppose that the random variables X and Y have a joint density function given by: f(x,y) = {c(2x+y) for 2≤x≤6 and 0≤y≤5, 0 otherwise P(3 < X < 5, Y >1), P(X < 3), P(X +Y > 5), Find the joint distribution function (cdf),
Let X be a Gaussian random variable with zero mean and variance equal to 2. 1-Find the probability density function of the random variableY = 4X + 4 2-Find the probability P(Y>4).
The random variables X and Y have the following joint probability density function:f(x,y)={e−x−y , 0<x<∞; 0, elsewhere. What is Cov(X,Y)(X,Y)?
Let (X, Y ) be a random vector with joint density function of the form:f(X,Y )(x, y) = 24xy, 0 < x < 1, 0 < y < 1, x + y < 10 , otherwise(c)Compute the conditional probability P(X < 1/6|Y=1/2) and the conditional expectation E(X | Y = y)
Let X and Y be two independent random variables, X ∼ Γ(α, λ) and Y ∼ Γ(β, λ). Find the joint probability density function f(Z,W)of the vector (Z, W)(b) Show that Z and W are independent(c) Show that Z ∼ Γ(α + β, λ) and W ∼ B(α, β)

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS

Let be the random variable X with distribution function given by: Fx (x) = { x³ 1 a) Find the density function of X. b) find P[1sx5²/1 X 2 x ≤ 0 0 < x < 1 x ≥1 c) Find the expectation of X. d) Find the variance of X e) Find the standard deviation of X.