A random variable X has probability densityfunctionf(x;0) =H:0=10H₁H:0=2.10, elsewhereIt is desired to test the null hypothesisagainst the alternativeдеA. -1.6094- OxConsider the test which rejects Hif X≥c:0B. 1.2223What will be the value of c for which thelevel of significance of the test is 0.1.C. 2.3025x>0D. None of the above

Answered: A random variable X has probability…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a Gaussian random variable with mean equal to 3 and variance equal to 5, then the PDF of X has equal values at: O x = 5, x = -5 x = 1, x = -1 O x = 3, x = - 3 O x = -2, x = 2 O x = 2, x = 4
A random Variable X, from an unknown experiment produces the following Probability Mass Function Table: x 2 4 6 8 10 P(A) 1/4 a 1.8b 1:8 Given that the mean or the expected value of x is 6, E(x) = 6. Compute the coefficient of variation of the random variable x, CV(x)
A continuous random variable has the following p.d.f. f(x, 0) = 0xº-1 ,0 < x < 1 = 0 ,otherwise. Based on a single observation x, it is decided to reject Ho: 0 = 3 against H,: 0 = 2, if x < 0.7. Find the probability of type II error. %|
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.
Q9. Let us assuming the voltage output of a microphone is a Gaussian random variable V with expected value Hy = 0 and standard deviation ơy = 5 V. The microphone signal is the input to a limiter circuit with cutoff value ±10 V. The random variable W is the output of the limiter: 10 -10 V 10. W = g(V) = V -10 10 -10 10 V From this example, find the following A. Find the PDF of W? B. Find the CDF of W?
b) Let X to be a random sample from a distribution with a probability density function given by f(x; 0) = {0x0-¹,if 0 i) Find the level of significance of the test, a. ii) Calculate the power of the test.
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
Suppose the lifespan (in months) of a smartphone battery can be modeled as a continuous random variable with CDF F(x) = 1 − e-x/3 x ≥ 0 What is the probability that the battery lasts between 12 to 15 months?
Suppose random variable Y represents a random number generator that can take any value between 1 and 11. Then the density curve of the outcomes has constant height between 1 and 11, and height of 0 elsewhere. What’s the height of the density curve between 1 and 11? What is the probability that Y<2? What is the probability that Y=2? Can Y=2 happen as an event for this random number generator? What is the probability that Y=0? Can Y=0 happen as an event for this random number generator?
Let X be a normal random variable with mean 85 and a variance of 25 (i.e., X ∼ N (85, 25)). step1: Let M = aX + b for some constants a, b not equal to 0. Write an expression for the pdf of M . step 2: Suppose that X represents an approximate distribution of the final scores in a certain math course (ignore the fact that this approximation can technically have scores that are greater than 100 or less than 0). If the teacher were to curve the scores, it means he would determine a function to apply to the scores to achieve a desired distribution (assume an affine function in this case, as in the previous part). Suppose he wants the scores to be normally distributed with mean 80 and a standard deviation of 4. What should he choose for a and b? What students would see their score lowered, and what students would see their score increased?
a) Suppose that X is a random variable having the following probability density function given by (2(0-x) 02 f(x) = -, x > 0 (0, elsewhere Find the value of c such that an interval from x to cx is a (1- a)100% confidence interval for the parameter 0.
Consider a continuous random variable X with the following PDF: ſc −1≤x≤ 0 or 1 ≤ x ≤ 3 - {% otherwise (a) Sketch the PDF of X. Be sure to label your axes. (b) Determine the value of c that satisfies the normalization property. Set c to this value for the remainder of the problem. This can be done without integration, so your answer should be a number. fx(x)= (c) What is the expected value of X? (d) What is the variance of X? (e) What is E[2X² - 3X + 1]? (f) Calculate the probability that |X| is less than 2. (Your answer can be an integral, but you can also take advantage of the simple structure of the PDF.) (g) Let B = (-2,2). Determine the conditional PDF fx|B(x) of X given the event {X € B}. (h) Calculate the probability that X < 0 given that X is less than 2. (i) Calculate the conditional expectation E[X|B] of X given that |X| is less than 2.

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