Question

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).

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Given pdf and CDF . Now the property of pdf is

.

Now

That is is a strictly increasing function of over the interval .

Given the transformation .

The pdf of is

The distribution of uniform in the interval

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 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...
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....
Let X be a continuous random variable rv distributed via the pdf f(x) =4e^(-4x) on the...
Let X be a continuous random variable rv distributed via the pdf f(x) =4e^(-4x) on the interval [0, infinity]. a) compute the cdf of X b) compute E(X) c) compute E(-2X) d) compute E(X^2)
If X is a continuous random variable with pdf f(x) on the interval [a,b] then show...
If X is a continuous random variable with pdf f(x) on the interval [a,b] then show that a<E(X)<b.
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 ).
A continuous random variable X has pdf ?x(?) = (? + 1) ?^2, 0 ≤ ?...
A continuous random variable X has pdf ?x(?) = (? + 1) ?^2, 0 ≤ ? ≤ ? + 1, Where B is the last digit of your registration number (e.g. for FA18-BEE-123, B=3). a) Find the value of a b) Find cumulative distribution function (CDF) of X i.e. ?? (?). c) Find the mean of X d) Find variance of X.
A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 +...
A random variable X has the cumulative distribution function (cdf) given by F(x) = (1 + e−x ) −1 , −∞ < x < ∞. (i) Find the probability density function (pdf) of X. (ii) Roughly, take 10 points in the range of x (5 points below 0 and 5 points more than 0) and plot the pdf on these 10 points. Does it look like the pdf is symmetric around 0? (iii) Also, find the expected value of X.
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 X be a random variable with pdf f(x)=12, 0<x<2. a) Find the cdf F(x). b)...
Let X be a random variable with pdf f(x)=12, 0<x<2. a) Find the cdf F(x). b) Find the mean of X. c) Find the variance of X. d) Find F (1.4). e) Find P(12<X<1). f) Find PX>3.
Suppose X and Y are continuous random variables with joint pdf f(x,y) = x + y,...
Suppose X and Y are continuous random variables with joint pdf f(x,y) = x + y, 0 < x< 1, 0 < y< 1. Let W = max(X,Y). Find EW.
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT