Check whether the following can define probability distributions, and explain your answers.
a) fx=x12 for x=0,1, 2, 3, 4
b) fx=4-x27 for x=0, 1, 2
a) fx=15 for x=4, 5, 6, 7, 8
b) fx=3x+150 for x=1, 2, 3, 4,5
Check whether the following can define probability distributions, and explain your answers. a) fx=x12 for x=0,1,...
(15 pts) Determine the missing value(s) that would make the following valid probability distributions. (a) () ca2 ,4. Find c (b) (x) c(3x - 2) if 03. Find c for 0, 1.2,3
2.34. Probability integral transformation. Consider a random variable X with cumulative function Fx(x), 0-x-00, Now define a new random variable U to be a particular function of X, namely, U = Fx(X) For example, if FX(x)-1-e-Ax, then U = 1-e-Ax = g(X). Show [at least for reasonably smooth Fx(x)] that the random variable U has a constant density function on the interval O to 1 and is zero elsewhere. Hint: Con vince yourself graphically thatgg (u)- u and assume that...
Consider fx (x)=e*, 0<x and joint probability density function fx (x, y) = e) for 0<x<y. Determine the following: (a) Conditional probability distribution of Y given X =1. (b) ECY X = 1) = (c) P(Y <2 X = 1) = (d) Conditional probability distribution of X given Y = 4.
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
Please explain Let Z N(0,1), and let X = max(Z, 0) 1. Find Fx in terms of Φ(t). Ís X a continuous random variable ? 2. Compute p(X0) 3. Compute E(X) . Find the PDF fxa(u) 5. Compute V(X) (Hint: use fxa found above Let Z N(0,1), and let X = max(Z, 0) 1. Find Fx in terms of Φ(t). Ís X a continuous random variable ? 2. Compute p(X0) 3. Compute E(X) . Find the PDF fxa(u) 5. Compute...
4. The random variables X and Y have joint probability density function fx,y(x, ) given by: fx,y(x, y) 0, else (a) Find c. (b) Find fx(x) and fy (), the marginal probability density functions of X and Y, respectively (c) Find fxjy (xly), the conditional probability density function of X given Y. For your limits (which you should not forget!), put y between constant bounds and then give the limits for in terms of y. (d) Are X and Y...
question with answers, show steps: Given: fx,y(x,y)= (5/16)yx^2 for 0<y<x<2, determine: a) fx(x) by integrating y from 0 to x. Ans: fx(x)=(5/32)x^4 for 0<x<2 b) fy(y) by integrating x from y to 2 Ans: fy(y)=(5/48)y(8-y^3) for y<x<2 c) Test for independence using Criterion b Ans: Fails-> Not independent
A probability distribution function for a random variable X has the form Fx(x) = A{1 - exp[-(x - 1)]}, 1<x< 10, -00<x<1 (a) For what value of A is this a valid probability distribution function? (b) Find the probability density function and sketch it. (c) Use the density function to find the probability that the random variable is in the range 2 < X <3. Check your answer using the distribution function. (d) Find the probability that the random variable...
1. Consider a continuous random variable X with the probability density function Sx(x) = 3<x<7, zero elsewhere. a) Find the value of C that makes fx(x) a valid probability density function. b) Find the cumulative distribution function of X, Fx(x). "Hint”: To double-check your answer: should be Fx(3)=0, Fx(7)=1. 1. con (continued) Consider Y=g(x)- 20 100 X 2 + Find the support (the range of possible values) of the probability distribution of Y. d) Use part (b) and the c.d.f....
Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B. Distribution A: xi Distribution A: P(X=xi) Distribution B: xi Distribution B: P(X=xi) 0 0.02 0 0.49 1 0.09 1 0.24 2 0.16 2 0.16 3...