The volume of a cylinder is given by V = πr²h, where r is the radius of the cylinder and h is the height. Assume the radius, in cm, is lognormal with parameters μr = 1.6 and σ²r = 0.04 , the height, in cm, is log-normal with parameters μh = 1.9 and σ²h = 0.05, and that the radius and height are independent. a) Show that V is lognormally distributed, and compute the parameters μV and σ²V. (Hint: ln V = ln π+2 ln r + ln h.) b) Find P(V < 600). c) Find P(500 < V < 800). d) Find the mean of V. e) Find the median of V. f) Find the standard deviation of V. g) Find the 5th percentile of V. h) Find the 95th percentile of V.

Q: Assume the proportion of the time within a year, Y, and any flood by Kucuk Menderes River is…

A: Given: Y is the proportion of time within a year. fy=51-y4       0&lt;y&lt;10…

Q: The following table shows the rate of water flow (in L/min) through a dam. t(min) v'(t) (L/min) | 3…

A:

Q: Solve the solution of the DE of the Gompertz function: dP = c In[P dt М In[P

A: We have a nonlinear ordinary differential equation :

Q: Show that X ~ N(µ, o²) belongs to the 2-parameter exponential family of densities.

A: Given that X~Nμ,σ2

Q: # 1) If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt…

A:

Q: A log 5 m long is cut at 0.5-meter intervals and its cross-sectional areas A (at a distance x from…

A: This question is about mid point rule

Q: Suppose that y; has distribution N(0;,o² = 1). (a) Write the pdf in the natural exponential family…

A: (a)    According to question, yi~Nθi, 1 and Natural exponential family form given in question is,…

Q: Suppose Gabriel's Horn is built out of a material with nonuniform density, and assume the function…

A: The volume of a solid can be given as the product of the cross-sectional area and the thickness. The…

Q: Find a constant b > 0 so that the function e3x fx (*) = 0 < X <b 4 elsewhere is yalid density…

A:

Q: Suppose X - Exp(B) with density fx(x) = Bexp(-Bx) for a > 0 and B > 0. For Y = X/, where y> 0 is a…

A:

Q: Based on this histogram, the numerical kurtosis value for average handle time is most likely 25 5.0…

A:

Q: Find the normal line to f(x)=ax^2-3ax at x=2. Assume that a is a positive constant.

A:

Q: From 00 2 E (6) = 10° / 7 (1²57) ² exp [177] by evaluating the integral. dE, show that the average…

A:

Q: The following table shows the rate of water flow (in L/min) through a dam. t (min) 15 9 13 17 21 25…

A:

Q: Suppose fz(z) is a function given by So23 – 2) if -<<0 fz(2) = otherwise for a fixed constant c. Can…

A:

Q: Let "X" denote the tensile strength of a variety of metal samples with unit 107 Pa. Solve for the…

A: Solution

Q: An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement…

A:

Q: 9. Find the mass of a car antenna that is 3 ft long (starting at x = 0 and has a density function of…

A: 9. Given that a car antenna that is 3 ft long (starting at x=0) and has density function p(x)=3x+2…

Q: P (a, b) = So -at² _e-bt2 dt %3D t2

A:

Q: In one model of the changing population P(t) of a community, it is assumed that = - , where and are…

A: According to question, dPdt = dBdt-dDdt

Q: Let R be the rate at which customers are served in a queue. Suppose that R is exponential with pdf…

A: Given: Let R be the rate at which customers are served in the queue. The pdf of R is given as:…

Q: You study the relation between the log excess return on stock XYZ, denoted by Re XY Z,t, and the log…

A: Given the regression output of the log excess return on stock XYZ, denoted by Re(XYZ, t) and the log…

Q: Find the center of mass of the thin plate bounded by the graphs of the given functions. g(x) =…

A:

Q: (a) Is first order stationary (b) Has total average power of 61 W

A:

Q: The probability that a radioactive substance will decay at time t is modeled by the density function…

A: From the given information, the probability that a radioactive substance will decay at time t is…

Q: Suppose a spherical balloon grows in such a way that after t seconds, its volume V is given by V = 4…

A: The volume of the spherical balloon is ,

Q: The following table shows the rate of water flow (in L/min) through a dam. 15 9 t (min) V'(t)…

A:

Q: The edge of a cube is measured at 3 cm, with a possible measurement error of 0.2 cm. Use…

A:

Q: Suppose that a person’s score X on a mathematics aptitude test is a number between 0 and 1 and that…

A: A person’s score X on a mathematics aptitude test is a number between 0 and 1. A person’s score Y on…

Q: A cylindrical wire of radius R elongates when subjected to a tensile force F. Let Lo represent the…

A:

Q: Find the normal line to f(x) = ax - 3ax at x=2. Assume that a is a positive constant. %3D

A: Given: f(x)=ax2-3ax &amp; x=2 To determine: Equation of normal line to given f(x)

Q: suppose the cdf of r.v. X is given by 1- e -2 x x > 0 F(x) = x < 0 Please find its pdf, and compute…

A: It was stated to suppose that X is a random variable. The given CDF is as follows:  Fx=1-e-2x ;…

Q: Find the mean and variance of the gamma distribution using integration to obtain E(X) and E(X2).…

A: Gamma function is defined as: γα=∫0∞xa-1e-xdx Divide both sides by γα…

Q: Q1. The coefficient of rigidity (n) of a wire of length (L) and uniform AL diameter (d) is given by…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Let g(t) = cos (nt). Compute the average value of g(t) over the interval IN

A:

Q: (b) Show that Y = log () is exponentially distributed with rate parameter 0, that is, the pdf of Y…

A: Solution

Q: 9. Find the mass of a car antenna that is 3 ft long (starting at x = 0) and has a density function…

A: Given that a car antenna is 3 ft long (starting at x=0) and has a density function of ρ(x)=3x+2…

Q: Let f(x) = e2sinx. Use the local linear approximation of fat x = 0 to approximate e²

A:

Q: Let X and Y be independent exponentially distributed RVs with parameters A and respectively. Use the…

A: Solution is given below

Q: Consider quasi-one-dimensional isentropic flow of a perfect gas through a variable-area channel. The…

A: The Newton-Raphson Method is used to solve the equation of the form f(x)=0.  This is an…

Q: a) the linear approxinma ion to the function + 3X ät

A:

Q: Find the net change in ve]locity over [1, 4] of an object with a(t) = 8t − t2 m/s2.

A:

Q: In the article “Influence of Crack Width on Shear Behaviour of SIFCON” (C. Fritz and H. Reinhardt,…

A:

Q: Suppose that X follows the Weibull distribution with pdf f(r) = Br-1e on r>0, %3D where B> 0. (a) By…

A:

Q: Suppose that X and Y have joint density given by: f (x, y) = 15x²y, 0 < x < y < 1. (a) Find the…

A:

Q: A log 15 m long is cut at 1.5-meter intervals and its cross-sectional areas A (at a distance x from…

A:

Q: An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement…

A: Given Information: x¯=18.17 y¯=16.82 m=42 n=32 σ1=1.6 σ2=1.3 H0:μ1-μ2=0 versus Ha:μ1-μ2&gt;0

Q: Let f be a GPD density function with paramters & and B such that -(-+1) f(x) = B-1 (1+ where B > 0.…

A: From the given information, f be a GPD density function with parameters ξ and β such that…

Q: Find the normal line to f(x) = ax 8ax at x= 9. Assume that a is a positive constant.

A:

Q: Suppose a ball is thrown upward at time t = 0 with initial height X and initial upward velocity Y,…

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.