A continuous variable X defined on the interval (1, ∞) has p.d.f given by f(x) =...

Question

Question

A continuous variable X defined on the interval (1, ∞) has p.d.f given by f(x) = 1/x²

Derive the corresponding cumulative density function and graph it

math Statistics-And-Probability

Answer 1

Answer #1

The pdf or q random variable x is fx() e (, ) The cdt (cumulative distributi funchiom) is givm by Fr()PCx Sfrlt) dlt clt FrC

Answer 2

Similar Homework Help Questions

5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O...

5. (28 points) A continuous random variable X has probability density function given by f(x) = 3x^2,0<x< 1 O otherwise (c) What is the c.d.f. of Y = X^2 - 1? What is the p.d.f. of Y = X^2 - 1?
that E{E(Y|X) = E) (3 marks) If the random variable X has p.d.f. - SXSTE f(x)...

that E{E(Y|X) = E) (3 marks) If the random variable X has p.d.f. - SXSTE f(x) = {20 'o, otherwise, y = ex Gly)= Prob (Ys y) = Probe Prob(ancex) sluca inly) x < lncy F(x) dx = e cumulative distribution function technique to determine the p.d.f. of Y=e (4 marks CJE marks) avoy Given that the continuous random variable X and Y have joint p.d. f. f(x,y). She
Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed...

Suppose density function positively valued continuous random variable X has the probability a fx(x)kexp 20 fixed 0> 0 for 0 o0, some k > 0 and for (a) Find k such that f(x) satisfies the conditions for a probability density function (4 marks) (b) Derive expressions for E[X] and Var[X (c) Express the cumulative distribution function Fx(r) in terms of P(), the stan dard Normal cumulative distribution function (8 marks) (8 marks) (al) Derive the probability density function of Y...

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...
A continuous random variable Y has density function f(y) = f'(y) = 2 · exp[-4. [y]...

A continuous random variable Y has density function f(y) = f'(y) = 2 · exp[-4. [y] defined for -00 < y < 0. Evaluate the cumulative distribution function for Y Consider W = |Y| and find its C.D.F. and density Determine expected value, E [Y] Derive variance, Var [Y]
4. Let X be a continuous random variable defined on the interval [1, 10 with probability...

4. Let X be a continuous random variable defined on the interval [1, 10 with probability density function r2 (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is larger than 8 or less than 2 (this should be one number! (c) Find the probability that X is larger than some value a, assuming 1 < a< 10 d) Find the probability that X is more than 3

Part (a) (1 pt) Consider a continuous random variable X with density f(x). Suppose that the...

Part (a) (1 pt) Consider a continuous random variable X with density f(x). Suppose that the following three properties hold: • f(x) = 0 when x < 0 • f(x) = 0 when x > 0, for parameter 0 > 0 • f(x1) = f(x2) for all X1, X2 € (0,0). Find the density function f and the cumulative distribution function of X. Part (b) (1 pt) Find the methods of moments estimator of 0.
Give an example of a discrete or continuous random variable X (by giving the p.m.f. or...

Give an example of a discrete or continuous random variable X (by giving the p.m.f. or p.d.f.) whose cumulative distribution function F(x) satisfies F(n)=1-1/n! Thank you very much! Exercise 3.40. Give an example of a discrete or continuous random variable X p.d.f.) whose the cumulative distribution function F(x) (by giving the p.m.f satisfies F(n)1 - i for each positive integer n or
3. Let X be a continuous random variable defined on the interval 0, 4] with probability...

3. Let X be a continuous random variable defined on the interval 0, 4] with probability density function p(r) e(1 +4) (a) Find the value of c such that p(x) is a valid probability density function b) Find the probability that X is greater than 3 (c) If X is greater than 1, find the probability X is greater than 2 d) What is the probability that X is less than some number a, assuing 0<a<4?

(6) Consider the function f(x) = 1 2 x − 1 with its domain defined on...

(6) Consider the function f(x) = 1 2 x − 1 with its domain defined on the interval 2 ≤ x ≤ 4. (a) Draw the graph of f. (b) Verify that f is a probability density function for a continuous random variable X. (c) Compute P(X ≤ 3). (d) Compute P(X ≥ 3)