Gggnnnn Suppose X is an exponential random variable with mean parameterequal to 1.1Derive the distribution of Y = aX1/8, for a > 0, 3>0.Specify its density function. The distribution of Y is called aWeibull and we can write Y~Weibull(a. 3) where a isobviously a scale parameter.2 Derive the mean and variance of Y.Assume that the future lifetime (in years) of an iPhone follows aWeibull distribution with mean 8 and variance 320. Calculatethe probability that an iPhone fails within the first 5 years of use.

Deriving the Distribution of YWe are given:X ~ Exponential(1) (mean = 1)Y = X^(1/8)We need to find…

Answered: Suppose X is an exponential random…

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 4E

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The following table provides values of the function f(x,y). However, because of potential; errors in measurement, the functional values may be slightly inaccurately. Using the statistical package included with a graphical calculator or spreadsheet and critical thinking skills, find the function f(x,y)=a+bx+cy that best estimate the table where a, b and c are integers. Hint: Do a linear regression on each column with the value of y fixed and then use these four regression equations to determine the coefficient c. x y 0 1 2 3 0 4.02 7.04 9.98 13.00 1 6.01 9.06 11.98 14.96 2 7.99 10.95 14.02 17.09 3 9.99 13.01 16.01 19.02
Normal distribution. The moment generating function of a random variable U is M(t) = (1 - 8t)^-7. Find: i)Probability density function, ii)Mean, iii)Variance of U.
Let X∼Uniform(0,1) distribution. Find the PDF of Y= 3√X and derive the expected value and the variance of Y.
Suppose that Y1, . . . , Yn is a random sample from a population whose density function is
Ук. Suppose that Y₁. Y₂; Yn 15. 2 from Function random Sample a population with probability density f(y) = find the maximum BY 1-B B like hood ozy 21: B >0 Elsewhere Estimator of B
36. QUESTION: Let X have the density f(x) = 2x if 0 < r <1 and f(x) = 0 otherwise. Show that X has the mean 2/3 and the variance 1/18. Find the mean and the variance of the random variable Y = -2X + 3.
If X is a Gaussian random variable with mean zero and variance oʻ, find the pdf of Y = \X\.
Find the marginal PDFs of X and Y.
Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).
A density curve consists of the line segment connecting the points (0,1) and (0.5,1) and the segment connecting(0.5, 1) to the x-axis.a. Determine the coordinate point where the second segment crosses the x-axis.b. Determine the slope of that segmentc. Determine the equation of the line containing this segment (y = mx + b)d. Calculate the probability P(X > 1)
1.1. Suppose random variable X is distributed as normal with mean 2 and standard deviation 3 and random variable Y with mean 0 and standard deviation 4, what is the probability density function (pdf) of X + Y. 1.2. Let X and Y be independent standard normal random variables. Determine the pdf of W = x² + y². Find the mean and the variance of U = /W.
5. Let 0 and a be parameters. Show that the family of functions fo,a(x) = I > 0 (x+0)a+1³ is a probability density function. What can you say about the mean of a random variable that has fo,a as a pdf?

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