Problem 1: Calculate the expected value and variance for the rv whose pdf is given below. - 1 pt and 1.5pts respectivelyfi(l) =e-l(1+e-1)2for le R

To calculate the expected value and variance for the random variable rv whose PDF is given by…

Answered: Problem 1: Calculate the expected value…

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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answer item 4 only
2.4
Solve number 2 only
2. Suppose that in a certain chemical process the reaction time y (hour) is related to the temperature x (° F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y= 5 - 0.01x and the standard deviation o=0.075. a. What is the expected reaction time when temperature is 250° F? b. Suppose that five observations are made independently on reaction time, each one for a temperature of 250° F. What is the probability that all five times are between 2.4 and 2.6 hours?
Q.4. Annual depth of precipitation X (cm) is assumed to be lognormally distributed with u-50, o=10. What is the probability of the precipitation to remain in the range of 45 and 62 cm?
Compute for the variance and standard deviation of the population
Situation 9. Suppose that X has a lognormal distribution with parameters 0 = -2 and ² = 9. Determine the following: 18. P(500 x) = 0.1 20. The variance of X.
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5. Suppose the number of days it takes you to get a flu shot after it is available follows this equation: Y₂ = 30 - 2X₁ where y, is the number of days until you get the flu shot, and X, is the number of people you know who have the flu. Further, suppose on average you know 2.3 people who have the flu, with standard deviation 5. Suppose that the population has size m = 10. (a) Find the average time until you get the flu shot after it is available. (b) Find the standard deviation of time until you get the flu shot after it is available. (c) What is EY;?
Suppose μ₁ and ₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with two different types of braking systems. The data follows: m = 8, x = 115.6, $₁=5.09, n = 8, y = 129.5, and s₂ = 5.33. Calculate a 95% CI for the difference between true average stopping distances for cars equipped with system 1 and cars equipped with system 2. (Round your answers to two decimal places.) USE SALT Does the interval suggest that precise information about the value of this difference is available? O Because the interval is so narrow, it appears that precise information is available. O Because the interval is so wide, it appears that precise information is available. O Because the interval is so narrow, it appears that precise information is not available. O Because the interval is so wide, it appears that precise information is not available.
The type of battery in Jim's laptop has a lifetime X (in years) which follows a Weibull distribution with parameters a = 2 and B = 4. The type of battery in Jim's tablet has a lifetime Y (in years) which follows an exponential distribution with parameter ) =1/4. Find E(XY 2Y). (Answer as a decimal number, and round to 2 decimal places).

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Problem 1: Calculate the expected value and variance for the rv whose pdf is given below. - 1 pt and 1.5 pts respectively fi(l) = e-l (1+e-1)2 for le R