4.The cumulative distribution function of a continuous random variable, X is givenas follows:x<0F(x) =- x(x+4),320Sx<41x24(a)Calculate P(|X-1|<1).(b)Find the median.(c)Determine the probability density function of X. Hence, evaluateE(3X² -1).

From the given cumulative distribution function, we need to find the required probability value and…

Answered: 4. The cumulative distribution function…

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

If X is a continuous variable in the range 3 > X > 0 and its distribution function is as follows: F ( x ) = k : ( x3 + x2) find the probability density function?
If the probability density of X is given by f(x) =kx3(1 + 2x)6 for x > 00 elsewhere where k is an appropriate constant, find the probabilitydensity of the random variable Y = 2X 1 + 2X . Identify thedistribution of Y, and thus determine the value of k.
9.19 Let X and Y be two continuous random variables, with joint proba- bility density function f(x, y): - 30 -50x²-50y² +80xy for -
Suppose that the probability density function of x is fx=3x2, 0<x<1 0, elsewhere Determine p(x < (1/3)), p((1/3) ≤ x < (2/3)), and p(x ≥ (2/3)) Determine the cumulative distribution function of x.
suppose x has an exponential distribution with probability density function f(x) =2e^-2x, x>0. Then P(X>1)
Suppose that X is an exponential random variable with mean 5. (The cumulative distribution function is F(x) = 1- e-x/5 for x >= 0, and F(x) = 0 for x < 0. (a) Compute P(X > 5). (b) Compute P(1.4 <= X <= 4.2). (c) Compute P(1.4 < X < 4.2).
If X is a continuous random variable with X ∼ Uniform([0, 2]), what is E[X^3]?
If the probability density of X is given by f(x) =2x−3 for x > 10 elsewherecheck whether its mean and its variance exist.
If the joint probability density of X and Y is given by f(x, y) =⎧⎪⎨⎪⎩13(x + y) for 0 < x < 1, 0 < y < 20 elsewherefind the variance of W = 3X + 4Y − 5.
2)Let X1, X2, ..., Xn be a sample of n units from a population with a probability density function f (x I θ)=θxθ-1 , 0<x<1, θ>0 . According to this: Find the maximum likelihood estimator (MLE) of parameter θ.
10 - The cumulative probability function is given as follows. Find the Probability density function for a continuous random number 0 <x <6. A) F (x) = 12x +1/2 B) f (x) = (1/36) x +1/2 C) f (x) = (1/36) x +1/12 D) 0 TO) f (x) = (16) x +1/2
If the independent random variables X and Y havethe marginal densitiesf(x) =⎧⎪⎪⎨⎪⎪⎩12for 0 < x < 20 elsewhereπ(y) =⎧⎪⎪⎨⎪⎪⎩13for 0 < y < 30 elsewherefind(a) the joint probability density of X and Y;(b) the value of P(X2 + Y2 > 1).

SEE MORE QUESTIONS

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

4. The cumulative distribution function of a continuous random variable, X is given as follows: x< 0 F(x)=- -x(x+4), 32 Osx<4 1 x24 (a) Calculate P(|X–1|<1). (b) Find the median. (c) Determine the probability density function of X. Hence, evaluate E(3X² -1).