Problem #3: Let Z be the standard normal random variable.Problem #3(a):Problem #3(b):Problem #3(c):(a) Find the value of the probability density function fx(x) of X = |Z + 1 for x = 1.(b) Find the value of the probability density function fy(v) of Y = e² for y = 2.(c) Find E[Y] (Hint: this problem is closely related to the moment generating function for the normaldistribution.)Enter your answer symbolically,as in these examplesEnter your answer symbolically,as in these examplesEnter your answer symbolically,as in these examples

Given that Z~N(0,1). The PDF of Z is fZ(z)=12πe-z22 for -∞<z<∞. The CDF of Z is FZ(z)=P(Z≤z)…

Answered: Problem #3: Let Z be the standard…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.4: Hyperbolas

Problem 5ECP: Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.

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Problem #1: Suppose that the random variables X and Y have the following joint probability density function. f(x, y) = ce 6x-10y, 0 < y < x. Problem #1(a): Problem #1(b): (a) Find the value of c. (b) Find P(X< Y < 1) 4 Round your answer to 4 decimals.
(7) The median of the random variable X whose probability density function (3 3 = { 2x - ²x²,0 < x < 2², 0 , 0. W. is: (a) 0.5 f(y) = (b) 1 (c) 2 (d) 1.5
Problem #1: Choose a point uniformly at random in the unit square (square of side length one). Let D be the distance of the point chosen to the nearest edge of the square. Problem #1(a): Problem #1(b): Problem #1(c): (a) Compute PD > 0.15). (b) Let fo denote the probability density function of D. Evaluate fp(0.28). (c) Calculate E[D]. answer correct to 4 decimals answer correct to 4 decimals
3) Find the mean and variance of the random variable X with probability function or density f(x). (a)f(x)={k(1-x), –15xs1 O otherwise (b) ƒ(x) = k/3× , x = 1,2,3,... Note: in this problem, you need to first find the values of k.
Problem #1: Let X~ Unif[-2, 2], and Y = (X+ 1)². Problem #1(a): Problem #1(b): (a) Find fy() and fy(4), where fy() is the probability density function of Y. Separate your answers with a comma. (b) Find P{Y < 4}. Enter your answer symbolically, as in these examples Enter your answer symbolically, as in these examples
Problems 4.2. Suppose that X is a continuous random variable with probability density function given by f(x) = x² + x + } for 0
Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Suppose that X has the following probability density function (called the Rayleigh probability density function). Problem #8(a): Problem #8(b): f(x) = S (x10²) e-x2²/(20²) x > 0 o otherwise (a) If 0 = 96, find the probability that the vibratory stress is between 83 and 375. (b) If = 96, then 80% of the time the vibratory stress is greater than what value? Round your answer to 4 decimals. round your answer to 2 decimals
Problem 2. Let X be a random variable with probability density Jc(4x – 2x2), 0 < x < 2 f(x) = |0, otherwise (c) Calculate E[X]. (d) What is P(-0.1 < X < 0.4)?
Question 6 (a) Suppose X1 and X2 are independent, identically distributed exponential random variables with mean 1/A. Let U = (X1 + X2)/2 and V= X1. Find the joint probability density function of U and V, and also the conditional probability density function of V given that U = 1.
Problem 3.3: The joint probability distribution of the discrete variables X and Y is expressed in the table below. Find: (d) E[Y] (g) E[X/Y] (j) Cov(X,Y) (b) E[X] (e) E[Y²] (h) Var (X) (c) E[X²] (f) E[XY] (i) Var(Y) I f(x,y) 1.5 2.1 2.7 3.3 Y 0.46 0.088 0.031 0.073 0.021 0.86 0.057 0.066 0.085 0.022 1.26 0.084 0.065 0.096 0.030 1.66 0.036 0.073 c 0.089
2. A discrete random variable X has probability density function of the form (c(8 – x) for x = 0, 1, 2, 3, 4, 5 f(x) = otherwise. (a) Find the constant c. (b) Find P(X > 2). (c) Find the expected value E(X) for the random variable X.
Problem 4. Let fx (x) be the probability density function of X, which is given by fx(x) = - -2x ce 0, " x > 2 otherwise (a) Find the value of c to make ƒx a valid probability density function. (b) Calculate the cumulative distribution function (c.d.f.) of X. (c) Calculate P(12 < X ≤ 25) using the c.d.f. from part (b). You do not need to simplify your answer.

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