The continuous random variable X has probability density function (pdf)fx(x)20- 0 < x<0Show that the cumulative distribution function (cdf) of X is0 + xFx (x)- 0 x). The distribution function of the continuous random variable X is0,x< 3F(x) =1- kx 2 3x²a) Find the value of kb) Sketch the graph of F (x)c) Findi.Р(X < 4)ii.P(4 < X < 5)iii.Р(X > 6)d) Find the p.d.f of X

"Hello. Since your question has multiple parts, we will the solve first question for you. If you…

Answered: The continuous random variable X has…

Math

Probability

The continuous random variable X has probability density function (pdf) 1 fx(x) 20 - 0 x).

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

Related questions

Q: Suppose the cumulative distribution function of the random variable X is 0, x F(x)=0.25x + 0.4, 1.6…

A: Here given cumulative distribution function of RV X if : F(x)=0 ,…

Q: 6. The sick-leave time of employees in a firm in a month is normally distributed with a mean of 100…

A: mean = 100 hour standard deviation = 20 hours X = Sick leave time in hour

Q: Consider the continuous random variable with Cumulative Distribution Function (CDF) 0 for x 1)? Give…

Q: Scores on a certain standardized test, IQ scores, are approximately normally distributed with mean μ…

Q: The joint continuous distribution of random variables X and Y is given by f X,Y(x,y) = l2exp[-lx]…

Q: Let X be a discrete random that takes values from the set {-2,0,2} where P(X=x)= { 1/5 if x=-2 3/5…

A: From the given information we want to graph graph of cumulative distribution function.

Q: Suppose a discrete random variable X has cumulative distribution F(x)=,x=1,3,6,10, (a) Find Pr(X…

A: X is discrete variableCumulative distribution : F(x) =

Q: A random variable X has the following pdf where a is the only parameter. f(x) (1) Determine the…

A: As the line shown in figure passes through the origin and as the value of x increase the value of…

Q: Suppose that the unknown X is uniformly distributed between 0 and 1. What is the expected value of…

A: Given: X is distributed uniformly between 0 and 1 a=0 and b=1

Q: (a) A structure consists of 100 column footings. Suppose the settlement of each footing is…

A: Given that a structure consists of 100 column footings and the settlement of each footing is…

Q: Let X X -2x X be a random sample from exponential distribution with pdf f(x) = λe n 1' 2' Which is…

Q: The probability distribution of a discrete random variable X is given below: Value x of X P (X=x) -1…

Q: . Suppose the distance traveled in an ride-share trip in a certain area can be modeled by a random…

Q: The time it takes a person to wash the dishes is uniformly distributed between 10 minutes and 16…

A: Given, The time taken by person to wash the dishes is uniformly distributed between 10 minutes to 16…

Q: Distribution function of life span If F(t) = 1 – e¬At,2 > 0, find: a) Life function, sudden death…

A: Given the distribution function of life span as Ft=1-e-λt , λ>0

Q: A random variable has probability density function f(x) = 30x (1 - x) <(0 s xs 1). Compute its…

A: Use the formula for conversion from probability density function to cumulative distribution function…

Question

The continuous random variable X has probability density function (pdf)
fx(x)
20
- 0 < x<0
Show that the cumulative distribution function (cdf) of X is
0 + x
Fx (x)
- 0 <x<0
%D
20
Deduce an expression for P(X > x).

The distribution function of the continuous random variable X is
0,
x< 3
F(x) =
1- k
x 2 3
x²
a) Find the value of k
b) Sketch the graph of F (x)
c) Find
i.
Р(X < 4)
ii.
P(4 < X < 5)
iii.
Р(X > 6)
d) Find the p.d.f of X

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.

Similar questions

Question * Given X be the life time of a bulb having a probability density function f(x) =-e for x>0 and 0 elsewhere. The mean life time of the bulbs is equal to: %3D O 1/2 O None of these O 1/4 Question* Let X and Y be two independent continuous random variables with marginal distribution
9/10 Question * If the probability density function of random variable X is given by: - 1)(2- x), 0, 15 xS 2; otherwise. The value of k is equal to: None of these 3/2 7. 6. Question *
How do find the E[X^2].
For each random variable defined, describe the set of possible values for the variable, and state whether the variable is discrete or continuous. (a) U = number of times a surfer has to paddle in front of a wave before catching one (b) X = length of a randomly selected angelfish
PLEASE SHOW COMPLETE SOLUTION
The joint continuous distribution of random variables X and Y is given by f X,Y(x,y) = l2exp[-lx] for 0 < y < x < ∞ for some parameter l >0. = l2exp[-lx] * I[ 0 < y < x < ∞ ] Are X and Y independent? Explain. Identify the marginal distributions of X and Y by type and parameter values. (No conditioning-just state type of distribution)