The lifetime, X, of a particular integrated circuit has an exponential distribution with rate of λ=0.5 per year. Thus, the density of X is:f(x,x) = 1 e-^x for 0 ≤ x ≤ ∞o, λ = 0.5. λ is what R calls rate.Hint: This is a problem involving the exponential distribution. Knowing the parameter for the distribution allows you to easily answerparts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (notrecommended) you should be able to use the R integrate command with f(x) defined as above or with dexp() for all parts.d) What is the probability that X is greater than its expected value?e) What is the probability that X is > 5?f) What is the probability that X is> 10?g) What is the probability that X > 10 given that X > 5?h) What is the median of X?Please solution USING R script

Given rate=0.5 X~exp(rate=0.5) Note: According to Bartleby guidelines expert solve only one…

Answered: The lifetime, X, of a particular…

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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3 (4-x), 25x52 The error involved in making a certain measurement is a continuous rv x with pdf f(x) = b). Compute P(x > 0) c). Compute - 0 otherwise x > 0.5P(-1.2 (round to 4 decimal places) d). Compute P(x 0.5) (round to 4 decimal places)
Sketch the graph of each function. Intervals of Increase and Decrease Find each: b) d) Critical number Relative Maximum and Minimum values. y - x' + 4x - 5 S(x) - x' - 3x 2. fx) - x+ x- 4x' + 3 3. Sketch the graph and find the relative minimum for f(x) in the window (-1.2] X[-3,1]. 4. One model for the food-price index between 1984 and 1994 is the function: Kx) = 0.00009045x' + 0.001438x - 0.06561x' + 0.4598x - 0.627.x + 99.33 where x=0 corresponds to the year 1984. a) Sketch the graph in the viewing window [0,10] X [96,102] b) Estimate the times when food was cheapest and most expensive during this time period. 1. 5.
A microbiologist is testing an enzyme suspected to reduce the growth rate of a certain type of bacteria, and she wants to write a piecewise function to describe the effect she observes. She notices there is not a decrease in the size of the culture after the solution is applied, but that the growth rate decreases following its application. She is monitoring the changing mass of the culture because it is not practical to count individual cells, and she wants to model this with a continuous function representing the mass M (t) aft t hours, made up of two exponential growth functions of the form M (t) = aek. The bacteria culture is known to follow the growth model M (t) = 50e.032r for an initial sample of 50 grams. She allows the culture to grow unchecked for 48 hours before adding the experimental enzyme. She then finds that the mass of the culture 48 hours after application of the enzyme is about 546 grams. Use the limit definition of continuity to solve for the values of a and k that…
In economics the Lorenz curve is a function L(x) defined on the interval [0, 1] as follows. The x-axis is the proportion of people in a country’s population ordered from poorest to richest, e.g. x = 0.4 is the poorest 40% of the population, x = 0.9 is the poorest 90% – so all except the richest 10%. The y-axis measures the proportion of total income earned in the country.A point y = L(x) is on the Lorenz curve if the poorest 100x% of the population earn 100y% of the income. For example if L(0.6) = 0.35 then the poorest 60% of the population earn only 35% of the income in the country. It is always true that L(0) = 0 and L(1) = 1.If income is spread equally across the country, then L(x) is the straight line y = x. In such a country everybody earns the same. In reality the Lorenz curve is concave up and lies below the line y = x for all countries. The shaded area between y = L(x) and y = x measures how far income distribution is from being equal.The Gini coefficient for a country is…
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A company is manufacturing and selling towels. The marginal cost for producing towels is 0.15 CAD per towel. A market survey has shown that for every 0.10 CAD increase in the price per towel, the company will sell 50 towels less per week. Currently the company sells 1000 towels per week against the price that maximizes their profit. Determine the price of one towel? (Note: As usual, even though towels are only sold in integer units, assume we can use differentiable functions to describe the relevant quantities.)
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