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- Please answer number 3Find the average lifetime of the machine part. Calculate the probability that the lifetime of the machine part is less than 5.There are two Gaussian curves below (Plots A and B), along with the respective R source codes.Looking at the plots and the source codes provided, identify the parameters of respective Gaussian pdf's (probability density functions) and the numeric value of x in the PDF F(x)express the areas under the curves in terms of F(x). ( Do not calculate those areas.Your answers must be like F(x) or 1- F(x) for a relevant value of x.) Below is the source code and image for part B
- 4. The shelf life in days, for bottles of a certain prescribed medicine is a random variable having the density function 20,000 X >0 F (x) = {(x + 100)3’ 0, %3D elsewhere Find the probability that a bottle of this medicine will have a shelf life of a. at least 200 days b. anywhere from 80 – 120 daysThe 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 answer parts a,b,c and use the built-in R functions for the exponential distribution (dexp(), pexp(), qexp()) for other parts. Or (not recommended) 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 scriptBased on this density, what is the probability that X is between 0.5 and 1.5? Possible answers are 1/2, 1, 1/3, 3/4. Please show steps on how answer was obtained.
- According to a study, the maximum temperature T (in degrees Celsius) of each day during the spring has a distribution with the following function density: 21Please answer number 42. Assume that if a certain scale in a laboratory has been used too long without recalibration the probability density function of the measurement error is f(x) = 1 – 0.5x for 0Recommended textbooks for youA First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON
A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON