a=2.0207 b=2.302 need work Exercise 5-14 Consider a continuous random variable X with probability density function...
Find the mean of a continuous probability density function Question Consider a random variable X with probability density function given by f(x) for - 2 <3 < 2 otherwise. {$(4 – ) Calculate , the mean value of X. Provide your answer below:
22. Given a continuous random variable X with probability density function f(x) = {2x, if :05451 otherwise a. Find P(0.3< X< 0.6) b. Find the mean of X C. Find the standard deviation of X.
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)?
1. Let X be a continuous random variable with probability density function f(x) = { if x > 2 otherwise 0 Check that f(-x) is indeed a probability density function. Find P(X > 5) and E[X]. 2. Let X be a continuous random variable with probability density function f(x) = = { SE otherwise where c is a constant. Find c, and E[X].
b. Let X be a continuous random variable with probability density function f(x) = kx2 if – 1 < x < 2 ) otherwise Find k, and then find P(|X| > 1/2).
9. (14 points) Let X be a continuous random variable with probability density function Vix { Ook 1 2. otherwise (a) Sketch of the density function. Indicate P(x>) in your sketch. (b) Find P(X >). (e) Find the expected value, E(X). (d) Find P(X < _X >)).
4. Let X be a continuous random variable with probability density function: x<1 0, if if| if x>4 f(x) = (x2 + 1), 4 x 24 0 Find the standard deviation of random variable X.
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?
2. Suppose X is a continuous random variable with the probability density function (i.e., pdf) given by f(x) - 3x2; 0< x < 1, - 0; otherwise Find the cumulative distribution function (i.e., cdf) of Y = X3 first and then use it to find the pdf of Y, E(Y) and V(Y)
X is a continuous random variable, f(x) is the probability density function (pdf) of X, and F(x) is the cumulative distribution function of X. Then for any two numbers a and b with a < b, which of the following are true? Circle all correct answers. A. B. C. D. 5. If X is a normally distributed random variable with a mean of 36 and a standard deviation of 12, then the probability that X exceeds 36 is: A. .5000...