Problem #2: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to theloads is a1X₁ + a₂X₂.Problem =2(a)Problem =2(b)X1Problem #2(c):aX₂9Suppose that X₁ and X2 are independent random variables with means 2 and 5 kips, respectively, and standarddeviations 0.7 and 1.5 kips. respectively. Suppose that a₁ = 3 ft and a2 = 10 ft.(a) Find the expected value of the bending moment.(b) Find the standard deviation of the bending moment.(c) If X₁ and X₂ are normally distributed, what is the probability that the bending moment will exceed 82 kip-ft?answer correct to 4 decimalsanswer correct to 4 decimals

X is a random variable. The mean of X is defined as EX=∑xPX=x and the variance of X is defined as…

Answered: Problem #2: If two loads are applied to…

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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Problem 3. For i = 1,2, let X;,1,.. , Xị,n, consistute a sample of size n; from a population having unknown mean u and known variance of. For X; = +E, Xij, i = 1,2, a biostatistician suggests that the "optimal" estimator of the unknown parameter u is u = wiX1+ W2X2, where the weights are chosen so that the following two conditions are simultaneously satisfied: • E[f] = 4, i.e., the estimator is unbiased • Varſi), the variance of the estimator, is minimized. Derive explicit expressions for the particular choices of wi and wz that simultaneously satisfy these two conditions, and then interpret your findings.
Do ##2
Problem 2 The weights (in pounds) of 6 vehicles and the variability of their braking distances (in feet) when stopping on a dry surface are shown in the table. 5920 5350 6500 5100 5850 4800 Weight, x Variability in braking 1.73 1.94 1.88 1.55 1.62 1.50 distance, y 1) Complete to setup the hypothesis for the test. HO: P. На: Р. 2) Find the critical value(s). Use a=0.01 3) Calculate the test statistics t 4)Interpret your result
Problem 37.3 Let X be a gamma random variable with A = 1.8 and a = 3. Compute Pr(X > 3). Problem 37
Question 16 Express the null hypothesis Ho and the alternative hypothesis H1 in symbolic form. Use the correct symbol (u, p, o )for the indicated parameter. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, u, of 41°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Ο H μ 41ο. H1: H + 41° O Ho: us 41° H1: u > 41° Họ: H2 41° H1: H< 41° O Ho: H = 41° H1: H = 41° %3D
,Example 17-11. (a) Show that if a most efficient estimator A and a less efficient estimator B with efficiency e tend to joint normality for large samples, B-A tends to zero correlation with A. (b) Show that the error in B may be regarded as composed (for large samples) of two parts which are independent, the error in A and the error in (B -A). (c) Show further that V(A – B) = ( - 1)V(A). e
4. Continuous random variables X and Y are independent, with parameters ux = 30, ly = 40, Ox = 15, and ơy = 5. Which of the following gives the correct values for ux+Y and ox+y? = 70 and ox+y = 14.1 (A) Hx+Y (B) Мx+ү %3D 70 and o x+y %3D 15.8 (C) Hx+Y = 70 and ox+y = 20 (D) Ux+Y = -10 and ox+Y =14.1 (E) Ux+y =-10 and ox+y = 15.8
Do ##3
Problem 7 Let X ~ Poisson(a) and Y ~ Poisson(3) be two independent random variables. Define a new random variable as Z = X +Y. Find the PMF of Z.
Question 1
In this problem, we consider target detection in a radar system. Upon observing a realization a of the random variable X which represents the return signal in noise, a decision has to be made as to whether the target is present or absent. The target amplitude is known and equal to A > 0. The observation is made in zero-mean Gaussian noise W whose variance is known and equal to 2. If the target is present (hypothesis H1), X = A+W. If the target is absent (hypothesis Ho), X = W . The likelihood ratio test for this problem is stated as follows: If fi (x)/fo(x) > n= decide in favor of H1; otherwise, decide in favor of Ho.lf n = 1, determine the probability of correct detection (target declared present when indeed present) and the probability of false alarm (target declared present when in fact absent). Express these probabilities in terms of the ratio a = A/o. If a = 4, which of the following represents the correct probabilities of false alarm and correct detection, respectively? O None of…
Do ##5

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