f(x)=(1/B(α,β))*xα-1*(1-x)β-1 = | 12*x*(1-x)2 for 0<X<1 |
P(X>0.6) = f(x) dx = 12(x+x3-2x2) dx =12*(x2/2+x4/4-2x3/3)|10.6 =1-0.8208 =0.1792
The proportion of the maximum allowed time to complete a project is modeled as a beta...
Consider the completion time of a large commercial development. The proportion of the maximum allowed time to complete a task is modeled as a beta random variable with alpha -1 and beta-2. A) What is the probability that the proportion of the maximum time exceeds 0,7? B) Calculate the mean of this random variable?
Statistics - Please help! Thanks. 5. Let X be the random variable that describes the measurements of the diameter of Venus. We know that X is normally distributed with mean u = 7848 miles and standard deviation o = 310 miles. What is (a) P(x < 7000) (b) P(8000< x < 8100) (c) Verify your answers using R. 6. Assume the life of a roller bearing follows a Weibull distribution with parameters ß = 2 and 8 = 7,500 hours....
The maximum time to complete a task in a project is 1 month. Suppose that the completion time as a proportion of this maximum is a beta random variable with alpha-0,5 and beta -1. A) What is the probability that the task requires more than 0,5months to complete. B) Calculate the Variance of this random variable?
Gamma, Exponential, Weibull and Beta Distributions (Part 3) 1. The random variable X can modeled by a Weibull distribution with B = 1 and 0 = 1000. The spec time limit is set at x = 4000. What is the proportion of items not meeting spec? 2. Suppose that the response time X at a certain on-line computer terminal (the elapsed time between the end of a user's inquiry and the beginning of the system's response to that inquiry) has...
i need the answer to 6-c 5. A professor has a large class. The proportion of students who miss an assignment is a beta distribution with parameters with α and β 2. (a) Determine the probability that at least 70% of the students will miss an assignment. 6. Using the distribution given in problem 5 (b) What is the expected proportion of missed assignments? (c) What is the variance of this distribution? 5. A professor has a large class. The...
Recall that if X has a beta(a, B) distribution, then the probability density function (pdf) of X is where α > 0 and β > 0. In this problem, we are going to consider the beta subfamily where α-β θ. Let X1, X2, , Xn denote an iid sample from a beta(8,9) distribution. (b) The two-dimensional statistic nm 27 is also a sufficient statistic for θ. What must be true about the conditional distribution (c) Show that T* (X) is...
true or false Cycle time is the maximum time allowed for each workstation to complete its work on each unit.
The initial allele (an alternate form of a gene) proportions in a genetic simulation follow a beta distribution with α=4 and β=3. What is the probability that this proportion will exceed 60%? Find mean proportion. Find the most likely proportion (mode). Find the variance.
3. Sketch the graphs of the beta distribution having (to make it readable, please sketch the graphs separately but not to a combined figure) (a) α = 1 and β = 1, (b) α = 1 and β = 2, (c) α = 2 and β = 2, (d) α = 1 and β = 0.5, (e) α = 0.5 and β = 0.5, (f) α = 2 and β = 5.
The time to failure (in hours) of fans in a personal computer can be modeled by an exponential distribution with A= VUUS. Round your answers to 4 decimal places. (a) What proportion of fans will last at least 8000 hours? (b) What proportion of fans will last at most 7000 hours?