HomeworkLib
Question

Consider a continuous random variable X with the density function (exponential) ?(?)={?^−? ?? ?≥0 , 0...

Consider a continuous random variable X with the density function (exponential) ?(?)={?^−? ?? ?≥0 , 0 ??ℎ??????}
a) Find and sketch the CDF for X
b) Find the mean and variance of X (I want to see your calculation)
c) Find ?(1≤?≤2)

math   Statistics-And-Probability   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

(a) The probability density functi on of the exponential distributi on is 0; otherwise (1). e-%20 f (x) , otherwise The cumulative di stribution function is 1-e).xz0 0, otherwise 0, otherwise The mean of the exponential di stribution is E(X) 1 The rate parameter andisA-1 The Step-by-Step Instructions to obtain a Cumulative di stribution function using Excel 2010 * Select the x and F(x) in the columns of the Excel2010 spread sheet * Click Insert and then click Line-> 2D-Line * Click Layout7 * Write the heading The cumulative distributi on function,F(x * Write the heading of the X -axisis *Write the heading of the Y -axis is: CDF,F( * Click ok The cumulative distribution function using Excel 2010

The cumulative distribution,F(X) 0.8 L 0.6 0.4 0.2 F(X) 1 23 4 567 8 9

Interpretation:

The measures of the central tendency of the exponential distribution are mean and variance. The mean of the exponential distribution is E(X)=1, the parameter of the exponential distribution is lambda. The variance of the exponential distribution is Var(X)=1.

-------------------------------------------------------------------------------------------------------------------------------------------------

(b) The formula for calcul ating the mean of the continuous random variable(x)is Therefore, the mean is E[X)-1 The formula for calculating the mean of the continuous random variable(x)is The formula for caclulating the variance of X using the expectations is Var(X)=E(X)-| E(X Therefore, the variance of X is Var(X)-

(c) The probability that the random vari able is between 1 and 2 is 1-e-1+e 2-1 >e-1-e-2 0.367879441-0.135335 0.232544158 P(1sX S2)0.23254 Therefore, the probability that the random vaiable is between 1 and 2 is P (1SXS2)s |023254|

0 0
Add a comment
Know the answer?
Add Answer to:
Consider a continuous random variable X with the density function (exponential) ?(?)={?^−? ?? ?≥0 , 0...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions

  • is a continuous random variable with the probability density function (x) = { 4x 0 <=...

    is a continuous random variable with the probability density function (x) = { 4x 0 <= x <= 1/2 { -4x + 4 1/2 <= x <= 1 What is the equation for the corresponding cumulative density function (cdf) C(x)? [Hint: Recall that CDF is defined as C(x) = P(X<=x).] We were unable to transcribe this imageWe were unable to transcribe this imageProblem 2. (1 point) X is a continuous random variable with the probability density function -4x+41/2sxs1 What is...

  • (1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f()...

    (1) Suppose that X is a continuous random variable with probability density function 0<x< 1 f() = (3-X)/4 i<< <3 10 otherwise (a) Compute the mean and variance of X. (b) Compute P(X <3/2). (c) Find the first quartile (25th percentile) for the distribution.

  • For a continuous random variable X with the following probability density function (PDF): fX(x) = (...

    For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)

  • Consider a continuous random variable X with the following probability density function: Problem 2 (15 minutes)...

    Consider a continuous random variable X with the following probability density function: Problem 2 (15 minutes) Consider a continuous random variable X with the following probability density function: f(x) = {& Otherwise ?' 10 otherwise? a. Is /(x) a well defined probability density function? b. What is the mathematical expectation of U (2) = x (the mean of X, )? c. What is the mathematical expectation of U(z) = (1 - 2 (the variance of X, oº)?

  • A continuous random variable X has the probability density function f(x) = e^(-x), x>0 a) Compute...

    A continuous random variable X has the probability density function f(x) = e^(-x), x>0 a) Compute the mean and variance of this random variable. b) Derive the probability density function of the random variable Y = X^3. c) Compute the mean and variance of the random variable Y in part b)

  • 9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0...

    9.) Suppose that X is a continuous random variable with density C(1- if r [0,1 0 ¡f x < 0 or x > 1. (a) Find C so that px is a probability density function (b) Find the cumulative distribution of X (c) Calculate the probability that X є (0.1,0.9). (d) Calculate the mean and the variance of X 10.) Suppose that X is a continuous random variable with cumulative distribution function Fx()- arctan()+ (a) Find the probability density function...

  • 3. Let X be a continuous random variable with probability density function ax2 + bx f(0)...

    3. Let X be a continuous random variable with probability density function ax2 + bx f(0) = -{ { for 0 < x <1 otherwise 0 where a and b are constants. If E(X) = 0.75, find a, b, and Var(X). 4. Show that an exponential random variable is memoryless. That is, if X is exponential with parameter > 0, then P(X > s+t | X > s) = P(X > t) for s,t> 0 Hint: see example 5.1 in...

  • Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x)...

    Suppose that X is a continuous random variable with density pX(x) = ( Cx(1 − x) if x ∈ [0, 1] 0 if x < 0 or x > 1. (a) Find C so that pX is a probability density function. (b) Find the cumulative distribution of X. (c) Calculate the probability that X ∈ (0.1, 0.9). (d) Calculate the mean and the variance of X. 9.) Suppose that X is a continuous random variable with density C(1x) if E...

  • Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( )...

    Continuous RVs + Conditioned. The PDF of a random variable X is given by: ( ) ?? + 0.4, 0 ≤ ? ≤ 2 0, ??ℎ?????? a. Find the value C that makes fX(x) a valid PDF. (Hint: Draw the PDF to start.) b. Find and sketch the CDF, FX(x). c. Calculate P[X > 1] d. Let A be the event that X > 1. Find and sketch the conditional PDF fX|A(x|A).

  • 5. Find the moment generating function of the continuous random variable X whose a. probability density...

    5. Find the moment generating function of the continuous random variable X whose a. probability density is given by )-3 or 36 0 elsewhere find the values of μ and σ2. b, Let X have an exponential distribution with a mean of θ = 15 . Compute a. 6. P(10 < X <20); b. P(X>20), c. P(X>30X > 10), the variance and the moment generating function of x. d.

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT