Question

2. Let the probability density function (pdf) of random variable X be given by:                           ...

2. Let the probability density function (pdf) of random variable X be given by:

  

                        f(x) = C (2x - x²),                         for 0< x < 2,

                        f(x) = 0,                                       otherwise

    

  1. Find the value of C.                                                                           (5points)
  2. Find cumulative probability function F(x)                                       (5points)
  3. Find P (0 < X < 1), P (1< X < 2), P (2 < X <3)                                (3points)
  4. Find the mean, : , and variance, F².                                                   (6points)
Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and...
A continuous random variable X has the following probability density function F(x) = cx^3, 0<x<2 and 0 otherwise (a) Find the value c such that f(x) is indeed a density function. (b) Write out the cumulative distribution function of X. (c) P(1 < X < 3) =? (d) Write out the mean and variance of X. (e) Let Y be another continuous random variable such that  when 0 < X < 2, and 0 otherwise. Calculate the mean of Y.
Let the probability density function of the random variable X be f(x) = { e ^2x...
Let the probability density function of the random variable X be f(x) = { e ^2x if x ≤ 0 ;1 /x ^2 if x ≥ 2 ; 0 otherwise} Find the cumulative distribution function (cdf) of X.
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0...
Let X be a continuous random variable with probability density function (pdf) ?(?) = ??^3, 0 < ? < 2. (a) Find the constant c. (b) Find the cumulative distribution function (CDF) of X. (c) Find P(X < 0.5), and P(X > 1.0). (d) Find E(X), Var(X) and E(X5 ).
2. Let X be a continuous random variable with pdf given by f(x) = k 6x...
2. Let X be a continuous random variable with pdf given by f(x) = k 6x − x 2 − 8 2 ≤ x ≤ 4; 0 otherwise. (a) Find k. (b) Find P(2.4 < X < 3.1). (c) Determine the cumulative distribution function. (d) Find the expected value of X. (e) Find the variance of X
Let the probability density of X be given by f(x) = c(4x - 2x^2 ), 0...
Let the probability density of X be given by f(x) = c(4x - 2x^2 ), 0 < x < 2; 0, otherwise. a) What is the value of c? b) What is the cumulative distribution function of X? c) Find P(X<1|(1/2)<X<(3/2)).
Let X be a random variable with probability density function given by f(x) = 2(1 −...
Let X be a random variable with probability density function given by f(x) = 2(1 − x), 0 ≤ x ≤ 1,   0, elsewhere. (a) Find the density function of Y = 1 − 2X, and find E[Y ] and Var[Y ] by using the derived density function. (b) Find E[Y ] and Var[Y ] by the properties of the expectation and the varianc
The density function of random variable X is given by f(x) = 1/4 , if 0...
The density function of random variable X is given by f(x) = 1/4 , if 0 Find P(x>2) Find the expected value of X, E(X). Find variance of X, Var(X). Let F(X) be cumulative distribution function of X. Find F(3/2)
A random variable X takes values between -2 and 4 with probability density function (pdf) Sketch...
A random variable X takes values between -2 and 4 with probability density function (pdf) Sketch a graph of the pdf. Construct the cumulative density function (cdf). Using the cdf, find ) Using the pdf, find E(X) Using the pdf, find the variance of X Using either the pdf or the cdf, find the median of X
Let X be the random variable with probability density function f(x) = 0.5x for 0 ≤...
Let X be the random variable with probability density function f(x) = 0.5x for 0 ≤ x  ≤ 2 and zero otherwise. Find the mean and standard deviation of the random variable X.
Let X be a random variable with probability density function f(x) = {3/10x(3-x) if 0<=x<=2 .........{0...
Let X be a random variable with probability density function f(x) = {3/10x(3-x) if 0<=x<=2 .........{0 otherwise a) Find the standard deviation of X to four decimal places. b) Find the mean of X to four decimal places. c) Let y=x2 find the probability density function fy of Y.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT