3.29 An important factor in solid missile fuel is theparticle size distribution. Significant problems occur ifthe particle sizes are too large. From production datain the past, it has been determined that the particlesize (in micrometers) distribution is characterized by√3x¯4, x > 1,f(x) =10,elsewhere.(a) Verify that this is a valid density function.(b) Evaluate F(x).(c) What is the probability that a random particlefrom the manufactured fuel exceeds 4 micrometers?

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Answered: 3.29 An important factor in solid…

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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10. It is known that the probability of being able to log on to a computer from a re- mote terminal at any given time is .7. Let X denote the number of attempts that must be made to gain access to the computer. (a) Find the first four terms of the density table. (b) Find a closed-form expression for f(x). (c) Find P[X = 6]. (d) Find a closed-form expression for F(x). (e) Use F to find the probability that at most four attempts must be made to gain access to the computer.
An important factor in solid missile fuel is the particle size distribution. Significant problems occur if the particle sizes are too large. From production data in the past, it has been determined that the particle size (in micrometers) distribution is characterized by the following function. 7x8, x>1 f(x) = elsewhere (a) Verify that this is a valid density function. (b) Evaluate F(x). (c) What is the probability that a random particle from the manufactured fuel exceeds 3 micrometers?
A CI is desired for the true average stray-load loss μ (watts) for a certain type of induction motor when the line current is held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.1. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 56.0. watts (b) Compute a 95% CI for μ when n = 100 and x = 56.0. watts (c) Compute a 99% CI for μ when n = 100 and x = 56.0. watts (d) Compute an 82% CI for μ when n = 100 and x = 56.0. watts (e) How large must n be if the width of the 99% interval for u is to be 1.0? (Round your answer up to the nearest whole number.) n =
Please just answer part (7-IV). just the last part
Consider a group of people who have received treatment for a disease such as cancer. Let t be the survival time, the number of years a person lives after receiving treatment. The density function giving the distribution of t is p(t) = Ce-Ct for some positive constant C, and the cumulative distribution function is P(t) = , p(x)dx. Think carefully about what the practical meaning of P(t) is, being sure that you can put it into words. a) The survival function, S(t), is the probability that a randomly selected person survives for at least t years. Find a formula for S(t). b) Suppose that a patient has a 80 percent chance of surviving at least 2 years. Find C. c) Using the value of C you found in (b), find the probability that the patient survives up to (that is, less than or equal to) 1 years. d) Using the value of C you found in (b), find the the mean survival time for patients with this survival function, in years.
1. The sales tax returns of a business man is exponentially distributed with the density function given by -1Koo, f(x)= 100 x>0. What is the probability that his sales will exceed Rs.10,000 (perday), assuming that the sales tax is levied at the rate of 5% on the sales.
A CI is desired for the true average stray-load loss (watts) for a certain type of induction motor when the line current held at 10 amps for a speed of 1500 rpm. Assume that stray-load loss is normally distributed with = 2.9. (Round your answers to two decimal places.) (a) Compute a 95% CI for μ when n = 25 and x = 59.1. watts (b) Compute a 95% CI for when n = 100 and x = 59.1. watts (c) Compute a 99% CI for μ when n = 100 and x = 59.1. watts (d) Compute an 82% CI for when n = 100 and x = 59.1. watts (e) How large must n be if the width of the 99% interval for is to be 1.0? (Round your answer up to the nearest whole number.) n =
I need help with this, do I have the right answers?
Q. 2 Given fr(x) =kx’e ?; x20 (a) Find constant k so that it is a pdf; [Hint: Think about gamma distribution] (b) Does X have a x-distribution? If so, what is its degree of freedom? (c) Find E(X) and Var(X).
Suppose the life span of a laboratory animal is defined by a Rayleigh density function with a=0 and b=30 weeks: (x-a)² bu(x-a) Where £x (x)= = b (x-a)e 9 = { 1 u(x) = x>0 x < 0 What is the probability that the animal will live between 10 and 20 weeks? What is the expected lifespan of the animal?
A college professor never finishes his lecture before the end of the hour and always finishes his lectures within 2 min after the hour. Let X be the time that elapses between the end of the hour and the end of the lecture and suppose the pdf of X is fo fkr², if 0
1. Suppose that for a certain life the probability density function is x (*) 1+x ,x >0 X. Find (i) the survival function ofx (ii) the probability that the life aged 25 will die within next 15 years. (iii) the probability that the life aged 42 will die between 55 and 62.

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