(b) Let X be a continuous random variable with pdf given by: f(x) =c#x Find the...
2. Let X be a continuous random variable with pdf ( cx?, [xl < 1, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf f(x) = { cr", [w] <1, f() = 0. Otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(2) of X. (c) Use F(2) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ( cx?, |a| 51, f(x) = { 10, otherwise, where the parameter c is constant (with respect to x). (a) Find the constant c. (b) Compute the cumulative distribution function F(x) of X. (c) Use F(x) (from b) to determine P(X > 1/2). (d) Find E(X) and V(X).
2. Let X be a continuous random variable with pdf ca2, 1 f(x) otherwise, where the parameter c is constant (with respect to x) (a) Find the constant c (b) Compute the cumulative distribution function F(x) of X (c) Use F(x) (from b) to determine P(X 1/2) (d) Find E(X) and V(X)
LI CONTINUOUS DIST Let X be a random variable with pdf -cx, -2<x<0 f(x)={cx, 0<x<2 otherwise where c is a constant. a. Find the value of c. b. Find the mean of X. C. Find the variance of X. d. Find P(-1 < X < 2). e. Find P(X>1/2). f. Find the third quartile.
(22pts) 6. Suppose X is a continuous random variable with the pdf f(x) is given by $(x) = { 1 + 2 OSIS 1; Osasi otherwise. (4 pts) a Verify f(x) is a valid pdf. (4 pts) b. Find the cumulative distribution function (cdt) of X (4 pts) c. Find P(OSX30.5). (5 pts) d. Find E(X). (5 pts) e. Find V(x)
A continuous random variable, X, has a pdf given by f(x) = cx2 , 1 < x < 2, zero otherwise. (a) Find the value of c so that f(x) is a legitimate p.d.f. [Before going on, use your calculator to check your work, by checking that the total area under the curve is 1.] (b) Use the pdf to find the probability that X is greater than 1.5. (c) Find the mean and variance of X. Your work needs...
Let X be a continuous random variable with cumulative distribution function F(x) = 1 − X−α x ≥ 1 where α > 0. Find the mean, variance and the rth moment of X. Question 1: Let X be a continuous random variable with cumulative distribution function where a >0. Find the mean, variance and the rth moment of X
Problem 5. Let X be a continuous random variable with a 2-paameter exponential distribution with parameters α = 0.4 and xo = 0.45, ie, ;x 2 0.45 x 〈 0.45 f(x) = (2.5e-2.5 (-0.45) Variable Y is a function of X: a) Find the first order approximation for the expected value and variance of Y b) Find the probability density function (PDF) of Y. c) Find the expected value and variance of Y from its PDF Problem 5. Let X...
(a) Let X be a continuous random variable with the cdf F(x) and pdf f(.1). Find the cdf and pdf of |X|. (b) Let Z ~ N(0,1), find the cdf and pdf of |Z| (express the cdf using ” (-), the cdf of Z; give the explicit formula for the pdf).