Question

Suppose a r.v. X has pdf fX (x), cdf FX (x), and mgf MX (t). Which...

Suppose a r.v. X has pdf fX (x), cdf FX (x), and mgf MX (t). Which of these three functions would you use to compute the median value of this distribution? Explain why, and write one equation that you could use/solve to find the median.

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
Suppose that X has probability function fX(x)=cx2   for 0<x<1. (a) (5 pts) Find c. (b) (5...
Suppose that X has probability function fX(x)=cx2   for 0<x<1. (a) (5 pts) Find c. (b) (5 pts) Compute the cdf, FX(x). (c) (5 pts) Find P(-1 ≤ X ≤ 0.5) . (d) (5 pts) Find the moment-generating function(mgf) of X. (e) (10 pts) Use the mgf to find the values of (i) the mean and (ii) the variance of X.
3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0...
3. Let X be a continuous random variable with PDF fX(x) = c / x^1/2, 0 < x < 1. (a) Find the value of c such that fX(x) is indeed a PDF. Is this PDF bounded? (b) Determine and sketch the graph of the CDF of X. (c) Compute each of the following: (i) P(X > 0.5). (ii) P(X = 0). (ii) The median of X. (ii) The mean of X.
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf)...
Suppose a random variable X has cumulative distribution function (cdf) F and probability density function (pdf) f. Consider the random variable Y = X?b a for a > 0 and real b. (a) Let G(x) = P(Y x) denote the cdf of Y . What is the relationship between the functions G and F? Explain your answer clearly. (b) Let g(x) denote the pdf of Y . How are the two functions f and g related? Note: Here, Y is...
3.9 Suppose r.v. X has the exponential pdf f(x) = A exp[-. x], for x >...
3.9 Suppose r.v. X has the exponential pdf f(x) = A exp[-. x], for x > 0. and f(x) = 0. for x ? 0. Find Pr(x > a + b l x > a) given a, b > 0.
4. Consider a continuous random variable X which has pdf fX(x) = 1/7, 0 < x...
4. Consider a continuous random variable X which has pdf fX(x) = 1/7, 0 < x < 7. (a) Find the values of µ and σ^ 2 . (You may recognize the model above, and if you do, it is OK to simply write down the answers if you know them.) (b) A random sample of size n = 28 is taken from the above distribution. Find, approximately, IP(3.3 ≤ X ≤ 3.51). Hint: use the CLT.
Suppose you roll one eight sided die and let X denote the outcome. a) Find M...
Suppose you roll one eight sided die and let X denote the outcome. a) Find M (t) X (Show all work clearly. Hint… start by writing out the PDF) (no need to simplify the MGF!) [2] b) Use your MGF in part a to find the standard deviation of this distribution. (you must use the MGF method. You will receive no marks for finding the sd directly from the PDF)
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that...
Suppose that X is continuous random variable with PDF f(x) and CDF F(x). (a) Prove that if f(x) > 0 only on a single (possibly infinite) interval of the real numbers then F(x) is a strictly increasing function of x over that interval. [Hint: Try proof by contradiction]. (b) Under the conditions described in part (a), find and identify the distribution of Y = F(x).
Suppose X is a random variable with pdf f(x)= {c(1-x) 0<x<1 {0 otherwise where c >...
Suppose X is a random variable with pdf f(x)= {c(1-x) 0<x<1 {0 otherwise where c > 0. (a) Find c. (b) Find the cdf F (). (c) Find the 50th percentile (the median) for the distribution. (d) Find the general formula for F^-1 (p), the 100pth percentile of the distribution when 0 < p < 1.
Suppose that the moment generating function of a random variable X is of the form MX...
Suppose that the moment generating function of a random variable X is of the form MX (t) = (0.4e^t + 0.6)8 . What is the moment generating function, MZ(t), of the random variable Z = 2X + 1? (Hint: think of 2X as the sum two independent random variables). Find E[X]. Find E[Z ]. Compute E[X] another way - try to recognize the origin of MX (t) (it is from a well-known distribution)
Question 3 Suppose the random variable X has the uniform distribution, fX(x) = 1, 0 <...
Question 3 Suppose the random variable X has the uniform distribution, fX(x) = 1, 0 < x < 1. Suppose the random variable Y is related to X via Y = (-ln(1 - X))^1/3. (a) Demonstrate that the pdf of Y is fY (y) = 3y^2 e^-y^3, y>0. (Hint: Work out FY (y)) (b) Determine E[Y ]. (Hint: Use Wolfram Alpha to undertake the integration.)
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT