Let, f(x)= 1/15e-x/15, 0≤ x < ∞ be the p.d.f. of X i. find the c.d.f.,...

Question

Question

Let, f(x)= 1/15e^-x/15, 0≤ x < ∞ be the p.d.f. of X

i. find the c.d.f., F(x), for f(x).

ii. find the values of µ and ?².

iii. what is the moment generating function?

iv. what is the probability that 20<x<40?

v. what percentile is µ?

vi. what is the value of the 25th percentile?

math Statistics-And-Probability

Answer 1

Answer #1

For further queries comment.thank you.

Answer 2

Similar Homework Help Questions

Let X be a random variable with p.d.f. f(x) =(|x|+ 1)/15 forx=−2,−1,0,1,2,3. Find the moment generating...

Let X be a random variable with p.d.f. f(x) =(|x|+ 1)/15 forx=−2,−1,0,1,2,3. Find the moment generating function for X, and use it to find the mean and variance of X.
1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for...

1. Suppose that the p.d.f. of a random variable X is as follows: for 0<x<2, for 0 〈 x 〈 2. r for 0<< f(x) = 0 otherwise. Let Y - X (2 - X). First determine the c.d.f. of Y, then find its p.d.f. (Hint: when computing c.d.f., plotting the function Y- X(2 - X) which may help. )
Let x and y be random variables for which the joint p.d.f is as follows

Let X and Y be random variables for which the joint p.d.f. is as follows: f (x, y) = 2(x + y) for 0 ≤ x ≤ y ≤ 1, 0 otherwise.Find the cumulative distribution function (c.d.f.) of X and Y.Find p.d.f. of Z=X+Y.

Let X have the p.d.f. f(x) = 3(1−x)2 for 0 < x < 1. Find p.d.f....

Let X have the p.d.f. f(x) = 3(1−x)2 for 0 < x < 1. Find p.d.f. of Y = (1−X)3.
Please answer d,e,f and g, thank you! roblem 1. Let (U common p.d.f. i 1 be...

Please answer d,e,f and g, thank you! roblem 1. Let (U common p.d.f. i 1 be a sequence of ii.d. discrete random variables with f(k) for k = 1, 2, 3 and for n 21 let Sn = Σ,u. (a) Find the probability that S2 is even. (b) Find the probability that Sn is even given that S,-1 is even. (e) Find the probability that Sn is even given that S-1 is odd. (d) Let pn P(Sn is even). Find...
Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are independent. i. Find the PDF of Z- X +Y using convolution. ii. Find the moment generating function, øz(s), of Z. Assu...

Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are independent. i. Find the PDF of Z- X +Y using convolution. ii. Find the moment generating function, øz(s), of Z. Assume that s< 0. iii. Check that the moment generating function of Z is the product of the moment gen erating functions of X and Y Problem 3 Let X be Uniform(0,1) and Y be Exponential (1). Assume that X and Y are...

The random variable X has the following p.d.f. tx -9 - <I< an f(3) = 21...

The random variable X has the following p.d.f. tx -9 - <I< an f(3) = 21 0, otherwise Use the moment generating function technique to determine the p.d.f. of Y=X? Hence or otherwise state the mean and variance of the random variable Y. (6 Marks)
1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0 < 1, where...

1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0 < 1, where c is a constant. i) Find the constant c ii) What is the distribution function of X? ii) Let Y 1x<0.5 Find the conditional expectation E(X|Y). 1. (15 points) Let X be a continuous random variable with probability density function f (x) c(1-), 0
Let X be a random variable with p.d.f. f(x) = θx^(θ−1) , for 0 < x...

Let X be a random variable with p.d.f. f(x) = θx^(θ−1) , for 0 < x < 1. Let X1, ..., Xn denote a random sample of size n from this distribution. (a) Find E(X) [2] (b) Find the method of moment estimator of θ [2] (c) Find the maximum likelihood estimator of θ [3] (d) Use the following set of observations to obtain estimates of the method of moment and maximum likelihood estimators of θ. [1 each] 0.0256, 0.3051,...

Question 3 [10 marks Let W Then the p.d.f. 1 fw (w) 2"/21 (n/2) exp(-w/2) w3-1, w>0. and the c.d.f. is denot...

Question 3 [10 marks Let W Then the p.d.f. 1 fw (w) 2"/21 (n/2) exp(-w/2) w3-1, w>0. and the c.d.f. is denoted as Fw (w) (a) Show that 0, n > 0, and (i) The function fw(w) is a p.d.f. (i.e., that fw(w) 2 0 for w Jo fw(w)dw 1). (ii) The mode of W is n - 2 for n > 2. (b) As n oo, W becomes normally distributed with mean n and variance 2n. This has led...