2. For a laboratory assignment, suppose that the measurement error X of a certain physical quality...
Consider the random variable X whose probability density function is given by k/x3 if x>r fx(x) = otherwise Suppose that r=5.2. Find the value of k that makes fx(x) a valid probability density function.
Suppose a certain type of small data processing firm is so specialized that some have difficulty making a profit in their first year of operation. The probabil- Y that make a profit is given by 0, elsewhere (a) What is the value of k that renders the above a (b) Find the probability that at most 50% of the firns (c) Find the probability that at least 80% of the firins valid density function? make a profit in the first...
PLEASE SOLVE FULLY WITH NEAT HANDWRITING AND EXPRESS FINAL ANSWER WITH BOXES!! Suppose that the density (pdf) function for a random variable X is given by fx)or 0s x s2 and fx) 0 otherwise. What is Suppose that the density (pdf) function for a random variable X is given by f(x)--for 0 SX 2 and f(x)-0 otherwise, what is the probability P(0.5 1)? Round your answer to four decimal places. X Suppose that the density (pdf) function for a random...
Q. Suppose the joint probability density function of X and Y is (a) Show that the value of constant ?=12/11 (b) Find the marginal density function of X, i.e., fX(x). (c) Find the conditional probability density of X given Y = y, i.e., fX|Y(x|y). fxy(x, y) = s k(2 - x + y)x 1 0 0 < x < 1,0 = y = 1 otherwise
Q.4 (22') Suppose the joint probability density function of X and Y is fx,y(x, y) = { „) - k(2 - x + y)x 0 sxs 1,0 sys1 o otherwise (a) (7”) Show that the value of constant k = 12 (b) (7') Find the marginal density function of X, i.e., fx(x). (c) (8') Find the conditional probability density of X given Y=y, i.e., fxy(xly). 11
The error involved in making a certain measurement is a continuous rv X with the following pdf. f(x) = 0.09375(4 − x2) −2 ≤ x ≤ 2 0 otherwise (a) Sketch the graph of f(x). (b) Compute P(X > 0). (c) Compute P(−1 < X < 1). (Enter your answer to four decimal places.) (d) Compute P(X < −1.6 or X > 1.6). (Round your answer to four decimal places.)
The error involved in making a certain measurement is a continuous rv X with the following pdf. f(x) = 0.09375(4 − x2) −2 ≤ x ≤ 2 0 otherwise (a) Sketch the graph of f(x). (b) Compute P(X > 0). (c) Compute P(−1 < X < 1). (Enter your answer to four decimal places.) (d) Compute P(X < −1.2 or X > 1.2). (Round your answer to four decimal places.)
Suppose X and Y are two continuous random variables with probability density functions: fx(x)1 for 1<x2, fx(x) 0 otherwise, and fr (v) 3e3y for y>0, fr (y) 0 otherwise. a) Suppose X and Y are independent, is Z-X+ Y"memoryless"? Justify your answer. b) Suppose that the conditional expected value satisfies E(Y X)-X. Find Cov0), and El(Y-X) expX)]. Suppose X and Y are two continuous random variables with probability density functions: fx(x)1 for 10, fr (y) 0 otherwise. a) Suppose X...
The current in a certain circuit as measured by an ammeter is a continuous random variable X with the following probability density function: f(x) = {kx +.2, 3<x<5 0 otherwise a) what is the value of K b) what is the mean of x c) Fx(4) =
4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively. 4. Suppose that a two-dimensional random vector (X, Y) has a joint probability density function as 0.48y(2-x), 0 1,0 x y x f(x,y)- 0, otherwise Find two possible marginal probability functions fx(x) and fy(y) of X and Y, respectively.