Suppose X is an exponential random variable with parameter 1/2, and let Y = 14 X^2 + 7. Computethe value of the probability density function of Y at y=10. (Remember that exponential randomvariables only take nonnegative values!)TYPE YOUR ANSWER AS THE NEAREST TWO DIGIT DECIMAL NUMBER, AND USE e=2.72.

Given that X is an Exponential random variable with parameter 1/2. fx=12e-12x, x>0 Given that…

Answered: Suppose X is an exponential random…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The Exponential pdf for continuous random variable Y takes the form e-ylß y > 0 f(V) = for ß > 0. y 1.6) Give your answer to three decimal places.
How were the answers of 1.0000 and 54.5982 attained?
please answer only page 167 3.1.30
Suppose that the interval between eruptions of a particular geyser can be modelled by an exponential distribution with an unknown parameter 0 > 0. The probability density function of this distribution is given by f(x; 0) = 0e 0¹, x > 0. The four most recent intervals between eruptions (in minutes) are x₁ = 32, x₂ = 10, x3 = 28, x4 = 60; their values are to be treated as a random sample from the exponential distribution. (a) Show that the likelihood of based on these data is given by L(0) 04-1306 = (b) Show that L'(0) is of the form L'(0) = 0³ e 1300 (4- 1300). (c) Show that the maximum likelihood estimate of 0 based on the data is ~ 0.0308 making your argument clear. (d) Explain in detail how the maximum likelihood estimate of that you have just obtained in part (c) relates to the maximum likelihood estimator of for an exponential distribution.
Let X~Geo(0.3). Find the following a. P(X = k). b. P(1 ≤ X 3) and describe its interpretation. d. The mean μ = E(X) and the Variance σ2 = Var (X) of the random variable X.
5. Let X be a positive random variable; i.e., P(X - log(EX) (b) E[log(1/X)] > log[1/EX] (c) E (X³) > (EX)³
Exercise 10. For an exponential random variable X (Definition 10), show that E[X] = }. More generally, for a function o : R R, E(¢(X)] = | (u) dF(u) (5.4)

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