A random variable X has the pdf as f(x) = ax + b, for 0

Given,f(x)=ax+b ; 0≤x≤1E(X)=23

Answered: A random variable X has the pdf as f(x)…

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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(d) At any time, find the mean age of insects in the population. (e) Sketch g(x), the p.d.f. of the age distribution of insects in the population. (f) No calculations are required for this part of the question.Now suppose that a population with the life table function Q(x) thatyou obtained in part (b) is stable but not stationary. Describe brieflyhow the age distribution of the population would differ from that of astationary population with the same life table function if the populationis (i) growing, (ii) declining. Draw rough sketches to show what thep.d.f. of the age distribution might look like in each case.
3. ( interval (-2,6]. Here is the student's work: %3D A student used the Mean Value theorem on the function f(x) = |x - 1| on the (1) I calculated f(-2) = 3 and f(6) = 5. %3D (2) Then LO-[(-2) L(6)-f(-2) %3D %3D (3) By the Mean Value Theorem there is a number c in the interval (-2, 6] so that f'(c) = (The sentences have been numbered only to make it easier to refer to them.) For each sentence, explain why the student did that step. If there are any mistakes, tell the student what is incorrect about their work.
The height of an object t seconds after it is dropped from a height of 140 meters is s(t) = -4.9t² + 140. (a) Find the average velocity of the object during the first 5 seconds. m/s (b) Use the Mean Value Theorem to verify that at some time during the first 5 seconds of fall, the instantaneous velocity equals the average velocity. Find that time. S
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If f'(x) 7 OF(3) < 6 Of(3) < 2
Consider the function f(x)=1/x on the interval [1,8]. Find the average or mean slope of the function on this interval. By the Mean Value Theorem, we know there exists a cc in the open interval (1,8)(1,8) such that f'(c)f′(c) is equal to this mean slope. For this problem, there is only one cc that works. Find it. I have attempted to solve this problem but I feel like im off. I will show the work I have in a photo. Hoping to see where I went wrong.
Write an absolute value function f(t) to describe an individual variance from normal body temperature where t is the individual current temperature
cumulative distribution function for heights (in meters) of trees in a forest is F(x). (a) Explain in terms of trees the meaning of the statement F (7) = 0.5. F (7) = 0.5 tells us that i (b) Which is greater, F (7) or F (6)? Justify your answer in terms of trees. because every tree of height eTextbook and Media % of the trees in the forest have Same for stor meters also has height mete
I. Find: Solve the following ungrouped data. x-x (x-x)² 3 7 10 11 17 19 21 23 25 a. Mean b. Variance c. Standard Deviation d. Measure of Position D4 P45 Q3 D9 P85
(b) Let X represent the lifetime in months of a certain brand of light bulb. The pdf of X is given by f(x)=K(6-x), 0
Consider the function f(x) = on the interval [2, 12]. (A) Find the average or mean slope of the function on this interval, i.e. f(12) – f(2) 12 – 2 (B) By the Mean Value Theorem, we know there exists a c in the open interval (2, 12) such that f'(c) is equal to this mean slope. Find all values of c that work and list them (separated by commas) in the box below. List of values:
Prove variance property: var(aX +b) = a²var(X) where a and b are constants.

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A random variable X has the pdf as f(x) = ax + b, for 0 < x< 1. The mean of X is E(X) = 2/3. (1) Find a and b. (2) Find also E(X*) and Var(X). (3) Find the median of X. (4) Find P(0 < X < 0.5).