Question

1. Show that the median of continuous random variable with positive p.d.f. is uniquely defined. 2....

1. Show that the median of continuous random variable with positive p.d.f. is uniquely defined.

2. Exhibit an example of a continuous random variable for which the median is not uniquely defined.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Suppose that the p.d.f of a random variable X is as follows: f(x) = { c/(1−x)^1/2...
Suppose that the p.d.f of a random variable X is as follows: f(x) = { c/(1−x)^1/2 for 0 < x < 1 { 0 otherwise • Find the value of the constant c that makes f a valid probability density function. Sketch it. • Find the value of P(X ≤ 1/2)
Let X and Y are two continuous random variables. It's joint p.d.f is given as: f(x,y)...
Let X and Y are two continuous random variables. It's joint p.d.f is given as: f(x,y) = 2 , 0 < x < y < 1 = 0, otherwise Calculate P(x+y >1)
Suppose that the random variable X has p.d.f. f(x) = 1 − |x − 1|, if...
Suppose that the random variable X has p.d.f. f(x) = 1 − |x − 1|, if 0 ≤ x ≤ c 0, otherwise . (a) Find the value of c. (b) Find the probability that X > 0.5. (c) Find the mean and variance of the random variable X.
1 (a) Let f(x) be the probability density function of a continuous random variable X defined...
1 (a) Let f(x) be the probability density function of a continuous random variable X defined by f(x) = b(1 - x2), -1 < x < 1, for some constant b. Determine the value of b. 1 (b) Find the distribution function F(x) of X . Enter the value of F(0.5) as the answer to this question.
1. For which type of continuous distribution are the mean and the median always the same?...
1. For which type of continuous distribution are the mean and the median always the same? uniform and normal distributions only all of the above uniform distribution exponential distribution normal distribution 2. The skewness of a normal distribution is: negative zero positive something that varies 3. The standard normal probability distribution has a mean of ______ and a standard deviation of ______. 0, 1 1, 0 1, 1 0, 0 4. Any normal probability distribution can be converted to a...
Let X be a continuous random variable with the following probability density function: f(x) = e^−(x−1)...
Let X be a continuous random variable with the following probability density function: f(x) = e^−(x−1) for x ≥ 1; 0 elsewhere (i) Find P(0.5 < X < 2). (ii) Find the value such that random variable X exceeds it 50% of the time. This value is called the median of the random variable X.
A Lee uniform random variable (L), which is a continuous uniform random variable with a mean...
A Lee uniform random variable (L), which is a continuous uniform random variable with a mean of 0 and a standard deviation of 1. What is the equation for a Lee transformation, which transforms the continuous uniform random variable X~U(t, w) into L?
What is the difference between a continuous random variable and a discrete random variable? In your...
What is the difference between a continuous random variable and a discrete random variable? In your own words, do not copy from the internet. Please also give an example.
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.
i) show that the function f: Q->Q defined by f(x)=1/((x^2)-2) is continuous at all x in...
i) show that the function f: Q->Q defined by f(x)=1/((x^2)-2) is continuous at all x in Q,but that it is unbounded on [0,2]Q. Compare to the extremal value Theorem.