Let Y denote a random variable with the following cumulative distribution function.if y < 0Ina In (x + 1)²) if 0 < y < 1,if y > 1.F(y) :In(4)a. Find the PDF, ƒ(y).b. Evaluate P(Y = 0.5).c. Evaluate P(Y < 0.8|Y > 0.4).d. Evaluate P(Y < 1).

Name: Let Y denote a random variable with the following cumulative distribu
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Let Y denote a random variable with the following cumulative distribution function.if y 1.F(y) :In(4)a. Find the PDF, ƒ(y).b. Evaluate P(Y = 0.5).c. Evaluate P(Y 0.4).d. Evaluate P(Y < 1).

Answered: Image /qna-images/answer/e63a2ec1-bf29-4c1f-934f-55a0328b8407.jpg

Math

Statistics

Let Y denote a random variable with the following cumulative distribution function. { if y < 0 In(4 In((x + 1)²) if 0 < y < 1, if y > 1. F(y) a. Find the PDF, ƒ(y). b. Evaluate P(Y = 0.5). c. Evaluate P(Y < 0.8|Y > 0.4). d. Evaluate P(Y < 1).

Let Y denote a random variable with the following cumulative distribution function. { if y < 0 In(4 In((x + 1)²) if 0 < y < 1, if y > 1. F(y) a. Find the PDF, ƒ(y). b. Evaluate P(Y = 0.5). c. Evaluate P(Y < 0.8|Y > 0.4). d. Evaluate P(Y < 1).

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

A Consider that the variables X and Y have the following joint probability distribution. 1. 3. 0.05 0.05 0.00 0.05 0.10 0.20 0.10 0.35 0.10 (a) Find the marginal distribution of X (b) Find the marginal distribution of Y (c) Determine if X and Y are statistically independent. (d) Find P(Y = 1|X = 3).
Suppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X.
Q1. let Y₁ < Y₂ < Y3 < Y4 < Y5 are the order statistics of the random sample of size 5 from the distribution : f(x) = 3x², 0
Let random sample of n observations from each of the distributions: a. Poisson distribution with parameter θ. b. f(x, θ) = (1/ θ) e-x/θ , 0 < x. In each case find the Minimum Variance Estimator of θ and prove its efficiency.
2. The random variable X is the amount of fructose in apples (in ounces) grown at a local orchard and is represented by the following cdf: 2(x +), 1
(a) Let Y be a random variable distributed as X. Determine E(Y) in terms of r. (b) Let {X1, X2, . .. , Xn} be a random sample drawn from a normal distirbution with mean u and 1 variance o?. Denote S E-(X; – X)² as the sample standard deviation. Use the 1 n - result in part (a), or otherwise, to find E(S). (c) Find an unbiased estimator for the population standard deviation o.
Suppose the random variable X has the following PDF: 2 √2π This distribution is often called half-normal. Find E(X) and V(X). f(x) = , for x > 0.
Let X be a random variable with CDF x > 1 Fx(x) = 0 < x < 1 %3D x < 0 a. What kind of random variable is X: discrete, continuous, or mixed? b. Find the PDF of X, fx(x). c. Find E(ex).
The lifetime of a machine part has a continuous distribution: Osx<40 fylx) = (10+ x)? else a. Calculate the probability that the lifetime of the machine part is more than 6. b. Calculate the expectation of life of this machine C. Calculate the variance Calculate the probability that the lifetime of the machine part is more than 4 given that is lasts for less than 12 d.
1. Suppose that the PDF of X is given by 1+0.4x2 0< x <1 f(x) otherwise a. Find the expected value of X, E(X). b. Find the variance of X, Var(X). c. Find the standard deviation of X, Std(X)
In the daily production of a certain kind of rope, the number of defects per foot given by Y is assumed to have a Poisson distribution with mean λ = 3. The profit per foot when the rope is sold is given by X, where X = 60 - 4Y - y². Find the expected profit per foot. $ per foot
c) Consider the following table: i 1 2 3 4 5 6 7 8 9 10 R₁ 0.7329 0.9755 0.6761 0.0917 0.1584 0.2858 0.8564 0.3628 0.4337 0.5822 Assuming an M/M/1 setup, a service rate of 18 customers every 5 minutes, and a traffic intensity of 0.95 for a pdf characterized by the exponential distribution, compute the correpsonding variates.