Question 3 Suppose that the random variable X has the following prob- ability density function. f(x)...
Question 2 Let X be a continuous random variable that has a Cumu lative Distribution Function given by: Pr[X 20 if €(0,20). The CDF is zero for < 0 and one for x> 20. Find: a) Pr[X 10 b) Pr[X 5 e) E[X] d) The probability density function of r, f(x) 1 e) Plot (separately) a graph of the CDF of x and a graph of the pdf of as a function of r
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)
Suppose the random variable X has probability density function (pdf) - { -1 < x<1 otherwise C fx (x) C0 : where c is a constant. (a) Show that c = 1/7; (b) Graph fx (х); (c) Given that all of the moments exist, why are all the odd moments of X zero? (d) What is the median of the distribution of X? (e) Find E (X2) and hence var X; (f) Let X1, fx (x) What is the limiting...
QUESTION 3 Suppose that the density (pdf) function for a random variable X is given by f(x) = the probability P(0.5 SXs 17 Round your answer to four decimal places. for Os x s2 and f(x) = 0 otherwise. What is
4 (3 points) Suppose a random variable X has the following probability density function: 3x2 -1srs0 0 otherwise f(x) (a) Compute Pr[Xs-1/2 (b) Compute E (X), the expectation of x (c) Compute the cumulative distribution function of this random variable (for all real numbers).
19. A random variable X has the pdf f(x) = 2/3 0 otherwise if 1 < x 2 (a) Find the median of X. (b) Sketch the graph of the CDF and show the position of the median on the graph.
For a continuous random variable X with the following probability density function (PDF): fX(x) = ( 0.25 if 0 ≤ x ≤ 4, 0 otherwise. (a) Sketch-out the function and confirm it’s a valid PDF. (5 points) (b) Find the CDF of X and sketch it out. (5 points) (c) Find P [ 0.5 < X ≤ 1.5 ]. (5 points)
PLEASE SOLVE FULLY WITH NEAT HANDWRITING AND STATE THE FINAL ANSWER IN A BOX!!!!! Suppose that the density (pdf) function for a random variable X is given by f(X) = _ for 0 SX the probability P(0.5 1)? Round your answer to four decimal places. 2 and f(x)-0 otherwise. What is Suppose that the density (pdf) function for a random variable X is given by f(X) = _ for 0 SX the probability P(0.5 1)? Round your answer to four...
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...
Suppose the random variable X has PDF fX(x) = 3x2 when 0 < x < 1 and zero otherwise. What is the PDF of Y = 2X+3? a.Use the general method: Find the CDF of X and use it to get the PDF of Y b.Use a short-cut.