Consider the following exponential probability density function. 1(=) = for a>0 a. Which of the following is the formula for P(z < xo)?: 1 P(z < ®o) = e? 2 P(# < z0) = 1-e 3 P(z < zo) =1-e - Select your answer b. Find P(z < 1) (to 4 decimals). C. Find P(z 2 4) (to 4 decimals). d. Find P(r < 5) (to 4 decimals).
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- Suppose a random variable X has a probability density function given by O elsewhere f (x) = kx (1 − x) 0 ≤ x ≤ 1 0 elsewhere a. Find the value of k that makes this a probability density function b. Find P (0.4 ≤ x ≤ 1) c. Find P(x ≤ 0.4) d. Find P (0.8 ≤ x))Please help solve:Please solve this question
- The exponential distribution is a probability distribution for non-negative real numbers. It is often used to model waiting or survival times. The version that we will look at has a probability density function of the form p(y|v) = exp(-e¯ºy — v) (1) where y R+, i.e., y can take on the values of non-negative real numbers. In this form it has one parameter: a log-scale parameter v. If a random variable follows an exponential distribution with log-scale v we say that Y~ Exp(v). If Y~ Exp(v), then E [Y] =e" and V [Y] = e²v. 1. Produce a plot of the exponential probability density function (1) for the values y E (0, 10), for v = 1, v = 0.5 and v= 2. Ensure the graph is readable, the axis are labeled appropriately and a legend is included. ta il 2. Imagine we are given a sample of n observations y = (y₁,..., yn). Write down the joint proba- bility of this sample of data, under the assumption that it came from an exponential distribution with log-scale parameter v (i.e., write down the…Consider the following probability density function, what is the F(14) 0.22 x = 7 x = 9 x = 11 x = 13 x = 15 x = 17 0.22 0.05 0.05 f(x) = %3D 0.06 0.33 0.06 0.01 x= 19 x = 23For a given probability density function below, solve for "c" so that it becomes a valid pdf. {i x > 1 f (x) = x3 x < 1 5 O 6 O 4 none of these O 3
- 4. eBook Consider the following exponential probability density function. Answered Correctly for x20 If needed, round your answer to four decimal digits. (a) Choose the correct formula for Px S xo). (i) P(z S z0) =1+e (H) P(zs zo) = 1- (i) P(z< z4) = 1+e/7 (iv) P(z S z0) =1-e/7 Option (iv) (b) Find P(x S 2). 0.9867 (c) Find P(x 2 3). (d) Find P(x S 5). (e) Find P(2 sxS 5).The probability density function of X is given by f(x) = 6 – 2x, 2Question 2 The probability density function of the reliability of a piece of equipment is given by: a x)= a(162 – x²³) (x)=(a/1 16-x³ 0Recommended textbooks for youMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. FreemanMATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th…StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C…StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage LearningElementary Statistics: Picturing the World (7th E…StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman