Question

3. Suppose that a random variable X has the density function f (x) = 2x, 0...

3. Suppose that a random variable X has the density function
f (x) = 2x, 0 ≤ x ≤ 1,
and that f (x) = 0 for x <0 and x > 1.
a) Calculate the distribution function for X, as well as the corresponding E (X) and variance V (X).

b) The numbers ​​u1 = 0.0503, u2 = 0.9149, u3 = 0.3103, u4 = 0.1866, u5 = 0.6553
uniformly distributed, independent random numbers on the interval [0, 1]. Calculate, with justifications, five independent random numbers x1,. . . , x5 for the variable X. 
c) Calculate sample mean and sample variance for the simulated numbers for
X. Compare with the result in (a). (2p)
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 uniform random variable on (0,1), X, has density function f(x) = 1, 0 < x...
A uniform random variable on (0,1), X, has density function f(x) = 1, 0 < x < 1. Let Y = X1 + X2 where X1 and X2 are independent and identically distributed uniform random variables on (0,1). 1) By considering the cumulant generating function of Y , determine the first three cumulants 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.
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.
suppose x is a continuous random variable with probability density function f(x)= (x^2)/9 if 0<x<3 0...
suppose x is a continuous random variable with probability density function f(x)= (x^2)/9 if 0<x<3 0 otherwise find the mean and variance of x
5. Consider the random variable X with the following distribution function for a > 0, β...
5. Consider the random variable X with the following distribution function for a > 0, β > 0: FX (z) = 0 for z ≤ 0 ​= 1 – exp [–(z/a)β] for z > 0 (where exp y = ey) (a) Determine the inverse function of FX (z), where 0 < z < 1. (b) Let a = β = 2 for the random variable X, and define the numbers u1 = .33 and u2 = .9. Use the inverse...
6. A continuous random variable X has probability density function f(x) = 0 if x< 0...
6. A continuous random variable X has probability density function f(x) = 0 if x< 0 x/4 if 0 < or = x< 2 1/2 if 2 < or = x< 3 0 if x> or = 3 (a) Find P(X<1) (b) Find P(X<2.5) (c) Find the cumulative distribution function F(x) = P(X< or = x). Be sure to define the function for all real numbers x. (Hint: The cdf will involve four pieces, depending on an interval/range for x....
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)
Here are some vectors in R 4 : u1 = [1 3 −1 1] u2 =...
Here are some vectors in R 4 : u1 = [1 3 −1 1] u2 = [1 4 −1 1] u3 = [1 0 −1 1] u4 = [2 −1 −2 2] u5 = [1 4 0 1] (a) Explain why these vectors cannot possibly be independent. (b) Form a matrix A whose columns are the ui’s and compute the rref(A). (c) Solve the homogeneous system Ax = 0 in parametric form and then in vector form. (Be sure the...
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤...
Let X be a random variable with probability density function f(x) = { λe^(−λx) 0 ≤ x < ∞ 0 otherwise } for some λ > 0. a. Compute the cumulative distribution function F(x), where F(x) = Prob(X < x) viewed as a function of x. b. The α-percentile of a random variable is the number mα such that F(mα) = α, where α ∈ (0, 1). Compute the α-percentile of the random variable X. The value of mα will...
a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent...
a) let X follow the probability density function f(x):=e^(-x) if x>0, if Y is an independent random variable following an identical distribution f(x):=e^(-x) if x>0, calculate the moment generating function of 2X+3Y b) If X follows a bernoulli(0.5), and Y follows a Binomial(3,0.5), and if X and Y are independent, calculate the probability P(X+Y=3) and P(X=0|X+Y=3)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT