Question 5Let X1 and X, be random sample of normal distribution with mean 1 and 2 and variance 3 and 5respectively. What is the moment generating function of Y:3X1 + 2X2? Note that in theanswers below exp(x) = e® the exponential function with argument x.exp(7t + 23.5*(t^2))exp(7t + 19*(t^2))exp(7t + 47*(t^2))exp(7t + 9.5*(t^2))

Answered: Question 5 Let X1 and X2 be random…

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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When dealing with an unbiased estimator of population variance how should we define S^2?
Areas under normal distribution curves can be used calculate probabilities of many random variables in the natural and social sciences. The graph of the Standard Normal Curve, with a mean of 0 and a standard deviation of 1 is given below, and its function is given by 1 f(x) = √2T e 1 The integral of e dx would be used to calculate the probability of an event that occurs √2T -1.5 between -1.5 to 1.5 standard deviations from the mean. (-1.5, 0.13) 1 Unfortunately, √2π -1.5 methods to approximate the values. 1.5 -1.5 1.5 (-1, 0.24) Using Simpson's Rule, (-0.5, 0.35) e dx has no proper closed form antiderivative, so we must use numerical 1.5 -1.5 1-0.5 -0-2 Using the Midpoint Rule with three rectangles of equal width, dx 0 Using the Trapezoidal Rule with six trapezoids of equal width, (0, 0.4) 0.5 Round answers to 4 decimal places when appropriate. (0.5, 0.35) (1, 0.24) 1.5 Ibe 1.5 1.5 [ 13 e-t de = \ е 1.5 e-2 е dx (1.5, 0.13)
Q5 Find the variance for the PDF px(x) = e-«/2, x > 0.
What is the variance and standard deviation for the number of times the SAT is taken? x Frequency (f) fx f*x2= (f*x) x (x) (4) = (3)x(1) 5152727-(2547473)(2547473)/1518859=880035.3688/1518859=0.5794 (1) (2) (3)=(1)x(2) (4)=(3x1) Population Variance 1 721,769 721,769 721,769 2 601,325 1,202,650 2,405,300 3 166,736 500,208 1,500,624 4 22,299 89,196 356,784 5 6,730 33,650 168,250 Total 1,518,859 2,547,473 5,152,727 880035.3688 0.5794 n=1,518,859 ∑fx = 2,547,473 The population variance is 0.5794 The Standard Deviation? 0.76 Can you show me the steps to reach the standard deviation of .76 ?
Explain at least two differences between the following two point estimations of the population variance. 22 = Σ'1(X, – X)2 n-1 62 _ Σ 1 (X - X)2 =1 = n
Today, the waves are crashing onto the beach every 5.1 seconds. The times from when a person arrives at the shoreline until a crashing wave is observed follows a Uniform distribution from 0 to 5.1 seconds. Round to 4 decimal places where possible. The mean of this distribution is The standard deviation is The probability that wave will crash onto the beach exactly 1.4 seconds after the person arrives is P(x = 1.4) = The probability that the wave will crash onto the beach between 1.3 and 4.7 seconds after the person arrives is P(1.3 < x < 4.7) = The probability that it will take longer than 3.92 seconds for the wave to crash onto the beach after the person arrives is P(x > 3.92) = Suppose that the person has already been standing at the shoreline for 1.1 seconds without a wave crashing in. Find the probability that it will take between 2.4 and 3.8 seconds for the wave to crash onto the shoreline. 84% of the time a person will wait at least how long before the wave crashes in?…
Question 1.2 Consider the function f (x) = (1/24(x^2 +1) 1 < or = x < or = 4) = (0 otherwise) Calculate P (x = 3) Calculate P (2 < or = x < or = 3) Question 1.3 Consider the function f (x) = (k - x/4 1 < or = x < or = 3) = (0 otherwise) which is being used as a probability density function for a continuous random variable x? a. Find the value of K b. Find P (x < or = 2.5)
DCX Suppose that an airline quotes a flight time of 2 hours, 10 minutes between two cities. Furthermore, suppose that historical flight records indicate that the actual flight time between the two cities, x, is uniformly distributed between 2 hours and 2 hours, 20 minutes. Letting the time unit be one minute, (a) Calculate the mean flight time (x) and the standard deviation (ax) of the flight time. (Round your answers to 4 decimal places.) ux OX (b) Find the probability that the flight time will be within one standard deviation of the mean. (Round your answer to 5 decimal places.) P = 18 Fo MAR LO 5 li Ⓒ A WD Show
Question 5 Find the 82 -th percentile for a uniform random variable U with the lower limit 17 and the upper limit 21. The 82 -th percentile for U is (Round the answer to 2 decimal places)
Solve with R, please
Question 7 According to the data, the weight of a randomly selected checked-in luggage has a normal distribution with a mean of 51 lbs and a standard deviation of 9 lbs. Let X be the weight of a randomly selected checked-in luggage and let S be the total weight of a random sample of size 33. 1. Describe the probability distribution of X and state its parameters and o: X~ Select an answer (μ = Select an answer unknown X² B N T 2. Use the Central Limit Theorem and find the probability that the weight of a randomly selected checked-in luggage is less than 61 lbs. (Round the answer to 4 decimal places) Check-In Select an answer Select an answer the original population is normally distributed the sample size is large (n>30) although the distribution of the original population is unknown the sample size is small (n<30) and the distribution of the original population is unknown the distribution of the original population is unknown S~ Select an answer (s= Select an answer σ= to describe the…

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