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
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![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbd3c3147-011e-442a-8bf9-af3591b7ce73%2Fd50ed80d-e978-4b9b-9acc-7602a65f0492%2Fqg2eeu9_processed.jpeg&w=3840&q=75)
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- 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.Problem 3.9: The speed distribution function for N particles in a fixed volume is given by: AV (B-V) B3 where V (> 0) is the particle speed, and A and B are positive constants. Determine: (a) The probability density function F(V). (b) The number of particles N in the volume. (c) The minimum speed Vmin and maximum speed Vmax. (d) The most probable speed where the probability density function is the largest. (e) The average speed V and the root-mean-square average speed Vrms = √V² f (V) =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. (a) Compute P{D > 0.45}. (b) Let / denote the probability density function of D. Evaluate /p(0.36). (c) Calculate E[D].
- 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. (a) Compute P{D > 0.2}. (b) Let fp denote the probability density function of D. Evaluate fp(0.31). (c) Calculate E[D].Problems 4.2. Suppose that X is a continuous random variable with probability density function given by f(x) = x² + x + } for 0(Sec. 3.2) A student is required to enroll in one, two, three, four, five, six on the desired courseload) at a local university. Let Y the number of classes the next student enrolls themselves in. The probability that y classes are selected is known to be proportional to y+1, in other words the pmf of Y is given by p(y) = k(y+1) for y 1,...,7, and 0 otherwise (a) What is the value of k? or seven classes (depending (b) What is the probability that at most four classes are enrolled in? (c) What is the probability that a student enrolls in between three and five classes (inclusive)? y? /40 for y 1,.,7 be the pmf of Y? Explain why why not (d) Could p(y) orProblem #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). x > 0 f(x) = {(x10²) e-x²7/(20²) otherwise (a) If 0 = 108, find the probability that the vibratory stress is between 95 and 218. (b) If = 108, then 81% of the time the vibratory stress is greater than what value?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 decimalsProblem 2.4: A joint discrete probability function f (x, y) is expressed in the table below. Find: (а) с (b) P(1 < X < 3, 1.5 < Y < 1.7) (c) P(2.5 < X < 3.5) (d) P((X +Y) < 4.6) (e) the marginal distributions fx(æ) and fy(y) (f) whether the random variables X and Y are statistically independent. f(x, y) 2.1 3.7 2.9 1.56 0.01 0.05 0.07 y| 1.64 0.04 1.72 0.21 0.17 0.02 0.03Problem 2.6: A continuous joint probability distribution is expressed through the following expression. Find: (a) c, (b) P(X 1) (c) the marginal distributions fx(x) and fy (y) (d) whether the random variables X and Y are statistically independent. (e) f(y|x) (f) P(Y > 1.5|X = 1) Jcry for 0Problem 2.6: A continuous joint probability distribution is expressed through the following expression. Find: (a) c, (b) P(X < -0.2, 2 < y < 2.5), (c) P(-4 < X < -0.3), (d) the marginal distributions g(r) and h(y). x+y for -1Problem #7: Suppose that the random variables X and Y have the following joint probability density function. -10y, 0 < y < x. -3x - f(x, y) = ce (a) Find P(X < 2, Y < 10). (b) Find the marginal probability distribution of X.SEE MORE QUESTIONSRecommended textbooks for youTrigonometry (MindTap Course List)TrigonometryISBN:9781337278461Author:Ron LarsonPublisher:Cengage Learning
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