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):Problem #2(c):0X₁21X₂cSuppose that X₁ and X₂ are independent random variables with means 4 and 6 kips, respectively, and standarddeviations 0.8 and 1.3 kips, respectively. Suppose that a₁ = 7 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 104 kip-ft?answer correct to 4 decimalsanswer correct to 4 decimals

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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Question 1. Random variables X and Y take values in {1,2,3}. Their joint pmf is shown in the following table. Find E[XY] and E[Y|X]. X = 1 X = 2 X = 3 Y = 1 Y = 2 Y = 3 0.1 0 0.2 0 0.3 0 0.2 0.2 0
Question 3: a. Write R code to simulate n observations (X,Y) from the model: X~ N(0,5), Y|X- N (2X +3,3). (Hint: use rnorm to generate random variables from the normal distri- bution. b. Simulate 50 datasets for n = 30, and, for each dataset, fit a regression model (Y|X = Bo+ BiX+c). Make a histogram of the 50 estimates of 3₁. What are the sample mean and sample variance of these 50 estimates?
c,d,e
Problem #3: Let X₁, X₂, ..., Xn be a random sample from U(0, 0). Find the method of moments estimator of 8 and use it to estimate based on the following observed sample. 10.8, 27, 10.8, 27.2, 27.3, 25.2, 20.7, 24.2, 28.6 Problem #3: Just Savo answer correct to 2 decimals
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…
If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the loads is a₁X₁ + a2X₂. X1 21 Suppose that X₁ and X₂ are independent random variables with means 3 and 5 kips, respectively, and standard deviations 0.4 and 1.1 kips, respectively. Suppose that a₁ = 6 ft and a2 = 12 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 92 kip-ft?
Question 21: We have three independent random variables X₁, X2, and X3. Suppose that E(X)=0.4μ, Var(X₁)-2, E(X2) = 0.2μ, Var(X₂)=2, E(X3) = μ, Var(X3) = 5. Consider the point estimate: 5 2X₂ +7X3 a. Calculate the bias of the point estimate. Is i, unbiased? Explain. b. Calculate the variance of the point estimate ,. c. Calculate the mean square error of the point estimate if u=2.
Question # 4: Let Y = X2, and let X be a uniform RV over (-1,1), find the Linear Mean Square Estimator of Y in terms of X and its mean square error.
QUESTION 7 Given any random variable, X, E( Cov( X, 10) ) = OA. 0. OB. V(X). Oc. 10. D. none of the above. Click Save and Submit to save and submit. Click Save All Answers to save all answers. 20 000 esc F1 F2 F3 םםם F4 ! @ $ % 1 4 Q W E R tab # 3
Example 5.1 Consider two random variables X and Y with joint PMF given in Table 5.1. Table 5.1 Joint PMF of X and Y in Example 5.1 Y = 0 Y =1 Y = 2 X = 0 X = 1 Figure 5.1 shows PxY (x, y). JointPMF 3 伍 1 2 3 y Figure 5.1: Joint PMF of X and Y (Example 5.1). a. Find P(X = 0, Y < 1). b. Find the marginal PMFS of X and Y. c. Find P(Y = 1|X = 0). 1/00 1/6 1/6 loe
Problem #2: If two loads are applied to a cantilever beam as shown in the figure below, the bending moment at 0 due to the loads is a1X₁ + a₂X₂. Problem =2(a) Problem =2(b) X1 Problem #2(c): a X₂ 9 Suppose that X₁ and X2 are independent random variables with means 2 and 5 kips, respectively, and standard deviations 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 decimals answer correct to 4 decimals

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